STS-4
The STS-4 crew wore embroidered mission emblems on their escape suits and on their in-flight clothing.
These patches can be identified as a particular variant of the AB Emblem patch which has a distinct area of light red thread in the fold of the stripes behind the Shuttle near the center of the design. The more common version of the AB Emblem patch had red thread in this fill area.
It is questionable whether this particular patch variant can be classified as a true 'Crew Patch' since it appears to have been available commercially to at least some extent (as evidenced by an example seen on an NASM sale card).
However, it was the version worn by the crew and the version used in official post-flight presentations to NASA employees. This, combined with the fact that it does appear to be somewhat rarer than the regular AB version, makes it worthy of being considered a crew patch despite it having been available commercially.
The Crew Patch
STS-4 Crew Patch
This AB Emblem variant patch is just slightly smaller that the more common AB version but is most easily identified by the presence of a small fill area of distinctly lighter red thread in the flag stripes behind the Shuttle. Note that this coloration is also present in the much larger Lion Brothers patch.
Other Embroidered Mission Patches
A-B Emblem patch
The regular commercial AB Emblem patch is the one most commonly seen, and is recognisable by the lack of light red thread in the trail behind the Shuttle.
Lion Brothers patch
The Lion Brothers patch has a similar light red fill area to the AB version worn by the crew but the LB version is much larger. The reverse has a bare cloth back without a plastic or wax coating.
A-B Emblem red twill variant patch
Similar to the regular AB Emblem patch except that it has been embroidered on red twill (like the Lion Brothers patch) rather than the usual white. This can be seen exposed at the extreme edges of the patch. Overall the colors also look a little darker than the regular AB patch.
Swissartex patch
The vintage version of the Swissartex STS-4 mission patch is easily distinguished from the Lion Brothers and vintage AB versions by the thick red merrowed border. It is however almost identical to some later AB Emblem versions as shown below.
A-B Emblem curved text variant patch
This variant of the AB Emblem patch has the crew names running in a curve. Otherwise it is similar to the regular version.
A-B Emblem variant 2 patch
This later AB Emblem version of the patch has a thick merrowed edge added, making it virtually indistinguishable from the Swissartex version, although the crew name font is a little shorter in height in this patch.
A-B Emblem variant 3 patch
Apparently a later AB Emblem version of the patch, this one has somewhat taller lettering in the crew names, making it more similar to the Swissartex design.
Unknown manufacturer patch [STS4UNK1]
This patch has a very pale pink fill area in the trail behind the Shuttle and an overall design very similar to that of the crew patch. However this patch has a distinctive pale blue outer edge of exposed backing cloth and more importantly it is executed with very modern fill patterns throughout, marking it as a more recent product.
Apart from the modern fill patterns how can we be sure that this patch wasn't the one worn by the crew? In fact there are a couple of clearly visible traits that prove that this is not the version worn by the astronauts - the broad white border around the nose of the Shuttle and the fact that the "i" of "Columbia" in this patch looks more like an "l". If you look at closeup images of the crew wearing their patches it is clear that they weren't wearing this version of the patch.
Footnotes
[1] Example sales of STS-4 'crew' patches:
eBay item no. 150216364336 Feb 22, 2008, sold at $20.49 (with other patches)
eBay item no. 140400360084 Apr 25, 2010, sold at $27.45 (with other patches)
eBay item no. 160693797913 Mar 28, 2012, sold at $75 [in batch of patches with STS-3 crew patch too]
eBay item no. 220992001475 Apr 8, 2012, sold at $179.50 [on presentation certificate]
Direct private sales via AstroGallery web site Jun 2012 at $99 [several examples from Al Bishop collection]
eBay item no. 180961026683 Sep 2, 2012, sold at $100
eBay item no. 251159203315 Oct 5, 2012, sold at $108.50
eBay item no. 130784613658 Oct 21, 2012, sold at $75
eBay item no. 321015264852 Nov 6, 2012, sold at $91
eBay item no. 360521397585 Dec 2, 2012, sold at $78.77
eBay item no. 140901623371 Jan 6, 2013, sold at $75.97
eBay item no. 181075291927 Feb 8, 2013, sold at $137.50
eBay item no. 181093645130 Mar 6, 2013, sold at $99.99
eBay item no. 181260156379 Nov 15, 2013, sold at $39.99
eBay item no. 151266465308 Apr 5, 2014, sold at $8.50
eBay item no. 231227363151 May 16, 2014, sold at $23.72 [with another patch]
eBay item no. 281804659984 Sep 22, 2015, sold at $21.50
eBay item no. 381478853686 Nov 29, 2015, sold at $30.00
eBay item no. 81941123964 Feb 28, 2016, sold at $12.50
Space Walk Hall of Fame Charity Auction lot no. 221 Jun 17, 2017 sold as part of crew patch collection (STS-1, 3 & 4)
eBay item no. 292390572965 Dec 31, 2017, sold at $5.26 (with STS-1 & STS-3 crew patches)
eBay item no. 362213440539 Jan 18, 2018 sold at $25
eBay item no. 222953827781 May 5, 2018 sold at $18.50
eBay item no. 253942854045 Oct 20, 2018 sold at $9.99
eBay item no. 303647901141 Aug 13, 2020, sold at $132.12 with STS-1 and STS-3 crew patches
[2] Example sales of STS4UNK1 patches:
eBay item no. 230833432035 Sep 19, 2012, sold at $224.72
eBay item no. 181006585303 Oct 31, 2012, sold at $52.77