Do being anal and being an a**hole mean the same thing?

Not at all, but a person can certainly be both. 

Both are required to be approved as an answerMug moderator.

No.

The former comes from Freudian psychology. According to Freud, if a child became obsessed with hygiene during potty training, he or she would end up with an anal-retentive personality: perfectionist, attentive to detail, orderly, a control freak, anxious, and prone to constipation.

The latter is vulgar slang meaning either a person's anus or a stupid, irritating, or contemptible person. (O.E.D.)

I am very anal,
and for the purpose of this post
I don't mean in the sexual sense. 
I'll refer anyone to adultMug for discussions regarding those personal traits.

Bookworm was absolutely correct in how she summed it up. 
The terms anal-retentive and anal-expulsive are psychological in nature.
I think of those terms as being descriptive of the internal workings of a person,
such as our heart and mind..
The part of our development that makes us who we are.
The driving force behind the things we do.

Either personality type can be an azzhole though.
I tend to think of that term as being less inward in nature 
and more of an outward and rude expression of personality that is directed at others.