"The Hebrew word shachaq, commonly translated as skies, describes
things that were made firm or hardened through a casting type process. This helps to make sense of the word firmament which is related to the Hebrew word raqa (to beat, hammer out or spread out, e.g. metal). The heavens are like the finished goods of this manufacturing process. The language of Scripture not only hints at the heavens being like a fabric but suggests they are thin in a fourth spatial dimension, as observed by another author.
Strong
There are three verses that talk about the strength of shachaq:
Psalm 68:34—“Ascribe strength to God; His majesty is over Israel and His strength is in the skies [shachaq]” (NAS). God’s strength is in the shachaq!
Proverbs 8:28—“When He made firm the skies [shachaq] above, when the springs of the deep became fixed” (NAS). The verb used in relation to the skies means to strengthen, make firm or harden. This verse seems to be giving us a clue as to the changes that happened when God was creating the world.
Job 37:18—“Can you, with Him, spread out [raqa] the skies [shachaq], strong as a molten mirror?” (NAS). The word for molten is often translated as cast.
So again we see the Bible emphasizing the strength or hardness of 
shachaq. This verse also uses the word raqa (to beat, hammer out, or spread out, e.g. metal—see the next section on the firmament) to describe one of the activities God went through in making the shachaq.
Cast and hardened
Job 37:18 is not the only passage that mentions casting and hardening. In the very next chapter God questions Job in relation to creation, including a mention of shachaq:“Who can count the clouds [shachaq] by wisdom, Or tip the water jars of the heavens,When the dust hardens into a mass, And the clods stick together?” (Job 38:37–38, NAS).
The word translated as mass on the third line means a casting and is translated as such in its only other occurrence in Scripture (1 Kings 7:37). So the third line can be translated as “when the dust hardens in the casting”.
Usage of raqiya
Raqiya, the Hebrew word for firmament, is used 17 times in the Old Testament. Nine of these occurrences are in Genesis 1 and a further five occurrences are in Ezekiel.
On the fourth day the phrase “in the firmament of the heavens” (NKJV) is used to describe where the sun, moon, and stars are placed. Even though God named the firmament heaven in verse 8, the expanded phrase is still used.
--Either the author wanted to be very clear as to which firmament was being referred to, or the firmament belongs to, or is a part of, the heavens in some way—or both.
The word heaven on its own was not suitable to accurately and clearly describe where the sun, moon, and stars were placed.
On the fifth day a similar phrase is used to describe the place where the birds fly, “across the face of the firmament of the heavens” (NKJV).
In Ezekiel 1, the prophet has a vision where he describes various things:
four living beings,
four wheels,
the firmament,
and a man on a throne.
Verse 22 describes an object that has the likeness of a firmament. 
This firmament is above the heads of the living beings and the throne is above this firmament. This passage is not talking about the firmament of Genesis 1:6–8 but something that resembles it in some way.
This firmament is above the heads of the living beings and the throne is above this firmament. This passage is not talking about the firmament of Genesis 1:6–8 but something that resembles it in some way.
--Interestingly, the firmament is described as stretching out or extending over their heads, i.e. in a horizontal direction rather than in a vertical or radial direction. This same word (Hebrew natah) is used to describe the stretching out of the heavens—see the next section on the heavens.
Usage of raqa
The Hebrew word for firmament is related in the Hebrew to the verb raqa. It is used 11 times in the Old Testament.
Here is the range of meanings:
To beat, hammer, or spread out metal (e.g. Exodus 39:3).
To spread people out, to disperse (2 Samuel 22:43).
To spread out the earth above the waters—a reference to the third day in Genesis 1 (e.g. Isaiah 44:24).
To stamp one’s foot or feet (e.g. Ezekiel 25:6).
To spread out the skies [shachaq] (Job 37:18). (This verse was examined in the section on the skies.)
This verb is applied to the skies [shachaq] but never to the heavens. In fact, Isaiah 42:5 and Isaiah 44:24 contain the word raqa and mention the stretching out of the heavens.
However the earth is the direct object of raqa not the heavens. The heavens is the direct object of natah, instead. Isaiah, through divine inspiration, has selected one word to describe the spreading out of the earth above the waters and, within the same verse, another word to describe the stretching out of the heavens. The verb that the word for firmament is related to is not used to describe the stretching out of the heavens!
The heavens Stretched out
....17 verses as describing the spreading out of the heavens, 
nevertheless, the idea is clearly repeated, with the most common description using the Hebrew verb natah.
As pointed out in some of the references mentioned earlier, natah suggests spreading out or extending rather than the expansion or large scale stretching of some sort of elastic material.
There are three similes we should quickly look at before moving on to the next point.
The heavens are:
Stretched out [natah] like a curtain that is used in the tabernacle (Psalm 104:2). The word used here for curtain occurs 54 times in the Old Testament, 44 of these are in Exodus 26 and 36 for the tabernacle curtain. The Gershonites of the tribe of Levi were responsible for carrying these curtains from place to place.
Stretched out [natah] like a fine, thin curtain (Isaiah 40:22). This 
word for curtain [doq] is different to the one above and occurs only once in the Bible. It is some sort of fine, thin cloth. This noun is related to the verb to crush, pulverize or make into dust but it isn’t the same verb that shachaq is related to.
Spread out [Hebrew mathach] like a tent (Isaiah 40:22). This word for spreading out occurs only once in the Bible. However, a word for sack is related to this verb and occurs only in Genesis 42–44—the sacks that Joseph’s brothers used to carry grain. The tent mentioned in this verse refers to a nomadic tent made out of strips of black goats’ hair cloth, sewn together into one large piece.
The heavens:
--Can be torn, like tearing your garments to show grief or remorse (Isaiah 64:1).
--Will wear out like a garment (Psalm 102:26; Hebrews 1:11).
--Will be rolled up like a scroll or robe (Isaiah 34:4; Revelation 6:14; Hebrews 1:12).
--At the same time as this, all the host of heaven will rot away and wither (Isaiah 34:4).
Furthermore, Revelation 6:14 uses the Greek word apochorizo (apo from and chorizo to separate or divide) to describe the heavens separating from something.
--Will be shaken (Hebrews 12:26; Haggai 2:6; Isaiah 13:13) and the “powers of the heavens will be shaken” (Matthew 24:29; Mark 13:25; Luke 21:26).
--Will be changed, like changing clothes, swapping the current version with a new version that can’t be shaken (Psalm 102:26; Hebrews 1:12; 12:27).All but the first point refer to future events in the end times.
A fourth spatial dimension
The rolling up of the heavens (Isaiah 34:4; Hebrews 1:12; Revelation 6:14) strongly suggests that there is some dimension in which the heavens are thin and which, presumably, is the same direction that they will be rolled up into.
Assuming that there is a fourth spatial dimension, then the 
description of the spreading out of the heavens like a curtain or tent (i.e. material that is thin in one of its dimensions) may also be a description of some sort of unfolding in four spatial dimensions rather than just three.
---In terms of understanding the differences between the three words, here is a suggestion:
The name for skies [shachaq] ref lects a focus on the substance.
The name for firmament [raqiya] reflects a focus on the process.
The name for heavens [Hebrew shamayim, from “to be lofty”] reflects a focus on the placement.
The heavens occur over 400 times in the Old Testament, so it is by far the most commonly used term out of the three. The heavens are like the finished goods or final product of this manufacturing process." CMI/AlanPace
