What is the game in the header image?
That's from one of the Close Combat games.
Does anyone know what the differences (if any) are between the Matrix Close Combat titles and the GOG titles?
As for Win10, it looks like Close Combat: Gateway to Caen and Close Combat: Panthers in the Fog can run Win10 with no problems. But the others can only run in windowed mode. More info here:
Depends what you mean by "difference". Any game that is being sold via Matrix and GOG will probably be the same - it's just a different store. I don't think Matrix have been selling the original CC games before now though, so they probably partnered specifically with GOG to roll out the original games so it'd have more impact (than just launching it on their own store).
And then they're probably putting their own CC titles up for sale there as well, because why not? They sell things on Steam as well as their own store (and if you buy from their own store you get a steam key anyway, provided the game itself is on steam.)
In terms of individual games, I know some Matrix-era CC games (like Cross of Iron) are remakes of older CC games (so in this case, Close Combat III).
Hope that helps?