The 'NES Version' was the branding of the revision of the Nintendo Entertainment System for the UK release. The European (non-UK) version of the Nintendo Entertainment System, was not a 'NES Version'. Since European countries would mostly be compatible with the UK PAL system's output, it exists mostly to distinguish regions for hardware region lockout (like how DVDs/Blu-ray regions are numbered).
Notice how 'NES Version' appears on the UK Control Deck box, but not on the US one. If you search online you will find non-English Control Deck boxes which also lack the UK's 'NES Version' branding.
Image from Nintendo wiki
Also, 'NES Version' Nintendo systems have 'NES Version' printed on the cartridge cover flap:
Image by The National Media Museum, Bradford.
Other versions include: no version name (for US), 'Mattel Version' (compatible with 'NES Version'), 'Hong Kong Version' (seen on both grey boxy NESes and Family Computers), 'Korean Version', 'Asian Version', 'European Version', 'Spanish Version' and 'Italian Version'. Notice how the UK Control Deck box photo incorrectly shows a NES system without 'NES Version' printed on its cover flap. :P
The following explanation from the Contra wiki lists several lockout regions including the US, the UK ('NES Version') and non-UK (not 'NES Version'):
The original NES (but not the top-loading NES-101) contained the 10NES lockout chip, which significantly increased the challenges faced by unlicensed developers. NES consoles sold in different regions had different lockout chips, so games marketed in one region would not work on consoles from another region. Known regions are: USA/Canada (3193 lockout chip), most of Europe (3195), Asia (3196) and UK, Italy and Australia (3197). Since two types of lockout chip were used in Europe, European NES game boxes often had an "A" or "B" letter on the front, indicating whether the game is compatible with UK/Italian/Australian consoles (A), or the rest of Europe (B). Rest-of-Europe games typically had text on the box stating "This game is not compatible with the Mattel or NES versions of the Nintendo Entertainment System". Similarly, UK / Italy / Australia games stated "This game is only compatible with the Mattel or NES versions of the Nintendo Entertainment System".
Nerdly Pleasures gives the following correspondence between lockout chip number and version.
NES NTSC
CIC 3193 or 3193A or 6113 or 6113A or 6113B1
United States (USA)
Canada (CAN)
Brazil (unconfirmed)
NES PAL-A "Mattel PAL Version" or "NES Version"
CIC 3197A
United Kingdom (UKV)
Italy (ITA)
Australia (AUS)
NES PAL-B "European Version"
CIC 3195A
Scandavia (SCN)
Sweden (SWE)
Netherlands (HOL)
European Economic Community (EEC)
Spain (ESP)
Germany (NOE or FRG)
France (FRA)
NES PAL "Hong Kong Version" and "Asian Version"
CIC 3196A
NES NTSC "Comboy" or "Korean Version"
CIC 3195A
As for what the letters 'NES' stand for, someone else may know. I don't have the original manuals, adverts or press releases to hand. My guess is that it's a meaningless acronym-word derived from 'Nintendo Entertainment System' just to quickly create an original distinct name, but it could be equally some other unknown random meaning like 'Nintendo European Sector' for example.
