Welcome!
I think the two very much cross. The games differ fundamentally in that poker deals with probabilities of outcomes due to incomplete knowledge--whereas chess is entirely deterministic--but these probabilities have set values just like chess pieces and positions do, which allows you (or a computer) to weigh and process that information in a way not unlike with chess. The basic game is different in its rules, of course, which will lend itself to a certain type of thinking compared to chess, but in much the same way that other deterministic games like Connect6, Havannah, or Breakthrough would. There's also a stronger element of psychology in poker, but again, it's present to a lesser degree in chess as well (understanding your opponent's strengths, weaknesses, and play style), and it's just another form of input based on an understanding of the subject.
I think one's skill in either game--and one's mind itself--can only be enriched by diversifying the tasks you try to solve.
I have two gaming addictions in life Chess and Poker (NLH). And I am by no means brilliant at either.
In recent times I have found that adapting my "chess brain" to the poker table has improved my results, I win more and consistently. By a chess brain I mean applying a cold logic to a game of poker.
This has raised a few questions for me...
Are there any GMs or top rated players especially good at poker? (Or vice versa)
Is there any ways to combine these two games?
Is there a real logic to poker, not exactly in the same way as a chess, but say for example could a computer programme be a strong/winning poker player?
All feedback welcome, this is my first post here :)