First, Are you aware of this replacement SSD for your system? OWC - SSD Upgrades for MacBook Air 11" & 13" Mid 2013, 2014, and 2015
As to using a Retina SSD in your Air system:
The SSD blade drive from the Retina system has a PCIe x4 interface which a newer than the PCIe x2 interface in your Air's.
While both are PCIe they are proprietary to Apple, we just don't know how interoperable they are. Their have been reports of people swapping out their older PCIe x2 SSD's within the MacBook Pro series with a newer PCIe x4. They reported an increase in performance!
I don't know if these are interoperable in your case. If the PCIe interface within the Air is a full Implementation then you should see better performance! I don't think you'll burn the SSD out by trying as you can see the connector in this image: SSDs from MacBook Air models from top to bottom: 2012-11", 2013-11", and 2013-13" yours being the middle one and this image from the Early 2015 MacBook Pro 13" PCIe x4 looks the same.
So unless you have one kicking around and was large enough for what you need I wouldn't waste the money getting the Apple SSD instead I would go with the OWC as its cheaper for the given size than the Apple unit.
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I had the exact same question. I bought a 2013 MBA with no SSD and had a spare 512GB SSD from a 2015 MBP that I wanted to use. Thankfully the SSD worked perfectly. Not only did it work, but the read/write speeds are amazing.
crwdns2934271:0crwdnd2934271:0 Ken Mor crwdne2934271:0
Which way you go is a big factor!
A newer SSD will play in an older systems (same I/O interface) But so far I've not found anyway to get an older SSD to play in a newer system (same I/O interface).
It appears the level of firmware on the SSD is the factor and Apple doesn't offer a way to update it beyond what the given system requires (thats assuming your older system still works).
crwdns2934271:0crwdnd2934271:0 Dan crwdne2934271:0