The difference is in the littoral definition of the two words.
Professional plays poker becaude it's their job. That's all the word means, in any field.
An amateur does something "for the love" of that thing.
Now, the likelihood of someone who does something professionally being better or more avcomplished at that thing than an amateur is higher, but it is not at all a certainty. There are terrible professionals in all jobs, and there are amazingly talented amateur musicians, artists, athletes, and even poker players. (And lots of former professional players who are now broke or on make up.)