When I started to learn hold'em in 2010 I used chess as sort of a base or foundation upon which I built off of.
I generally played chess with the same opponents and if you can imagine it doesn't take long to understand your opponent (myself included) so I had developed a revolving style to "mix up" my actions and confuse my opponent of what my intent was.
So if you gave me AA with the same stack size and same position on a full table you wouldn't get the same action from me continuously therefore making me harder to "read". As I learned more about hold'em I began to understand that there are certain "risks" involved with doing that and have recently been trying to break that habit.
So in conclusion, nothing similar between chess and poker except for some very broad concepts that would have been incorporated into your game as you became a better poker player anyways.
EDIT: I would also say the chess is more like billiards. Poker is a game of mathematics with odds
and percentages placed upon an assumed or determined value where as chess and billiards are games of geometry and use geometric equations to overtake your opponent.