As mentioned before, poker has a part luck while chess is 100% skills. Another difference is the amount of information available. With chess you have 100% information available (you can see everything, both your own as the opponents pieces), so it's a matter of being able to process all the information and make your decision based on that. The person that has enough knowledge about the game (at really high levels there is a marginal difference between the players) and is able to process the most information wins. With poker the situation is completely different. There is a big lack of information (you only know you cards and but not (all of) the opponents cards. So in this case you have to make a decision while not knowing everything. The person that can make the best decision based on the partially available information and can 'fill the gaps' will win.
The reason that a lot of poker players are also good chess players is probably because they like games. Probably they also like other kind of games where you have to use your brain.
Another game some poker players also enjoy is Magic the Gathering, which is more similar to poker than chess. There is a lack of information, there is a luck factor by not knowing which cards you'll get, but a skill in using the cards you get the best you can.