HJ's Basic business....101
a deal is a deal whether its documented or verbal.
Written contracts are generally better because they are more enforceable.
Playing for money, if its your main source of income means you are playing "professionally". (most professionals are top notch players, but that has nothing to do directly with them being defined as "professional".)
Most professional musicians play under contract and ( if you're playing in the USA) pay income tax .
Most semi-professional, part time, or just for fun players, can agree to play at a local venue without a written contract, hopefully without any adverse repercussions.
My personal advice to a self managed band leader is to discuss the policy concerning method of payment to the potential venue manager, determine if a written contract is necessary, and use your own judgment.
Union affiliation has its benefits, depending on the professional level that you're playing on.
(disclaimer) I ain't no lawyer, so take it for what its worth!
Howlin'