A good breakdown of the differences are given at http://forum.wotblitz.eu/index.php?/topic/24557-wotb-vs-wot-pc/. Key though is WOTB is bit easier to play with smaller maps, slightly slower speed, no artillery to knock you out from a distance, and things optimised for mobile players. WOT PC (Windows amd macOS) has rich detail in graphics and gameplay and is a bit harder to score XP. Gameplay is also a bit more detailed and has more to be considered with WOT PC (more attention to crew, consumables, etc are needed). You can play both for free but they are different battles so you really either go the WOT PC or the WOTB routes - gold, vehicles, XP have no relationship between the two versions.
The graphics on WOT PC is really stunning (I mean really stunning!) though and the maps are bigger that you play on, but games can last a bit longer vs WOTB which are average 5 - 7 mins. WOTB's big plus is also being able to include millions of mobile players (there is also an option to limit battles to players using similar controls to yourself ie. mobile or keyboard/mouse).
The interesting perspective for Linux players is that with Steam's new Proton compatibility WOTB will play as-is except the store and news functions are causing crashes. So, in theory, you can advance all the way with playing battles and scoring XP but don't try buy a premium tank as I did on the website as that tank is only for the PC version (I did get a refund tho).
On WOT PC I was surprised to find it worked quite well when I executed it's executable file using CrossOver for Linux (screenshot below shows it running on one of my screens with the second screen showing my Linux info - you can see the horizontal squashing and the graphics are lower resolution too). The only downside I found was that it squished the graphics a bit (which does not happen with the Blitz version). But the game was playing fine otherwise. I had installed the game using Windows 10 though and just ran the executable from the NTFS drive from Linux side. So I did not install it from Linux is side. Standard Wine did not execute but the fact that it ran with CrossOver says some tweaks may get it to go OK. Would be interesting if Steam Games could offer the PC version too.
In summary, though two different games with WOTB having a slightly more arcade approach that balances PC and mobile, whilst WOT PC has richer detail and graphics with a bit more to master. WarGaming has done a good job of bringing all the key elements to Blitz but it is worth knowing that you don't just switch between the two versions of the game.