You asked
Sigma 200mm f 2 dg os sports vs sony fe 135mm f 1 8 gm?
The Sigma 200mm f/2 DG OS Sports gives you more reach, and it has image stabilisation, which the Sony doesn't. I'd pick it for indoor sport and subjects that are far away. It also fits Sony E and L-Mount.
The Sony FE 135mm f/1.8 GM is shorter, so you get less reach, and it isn't stabilised. It's the better choice for portraits. For tight headshots and soft backgrounds, 135mm is a classic length, as the portraits guide explains.
So choose by subject: reach and stabilisation for sport, 135mm for people. If you're not sure which you'll shoot more, the wildlife and sport guide covers the telephoto side in more detail.
Written by Claude from this site's pages.