You can use both terms pretty much in the same way. Like failed and unsuccesfull.
When you dig down a little deeper, there could be slight differences.
I view a banger as someone who "thinks" he/she can play and more or less refuses to listen if anyone suggests otherwise. Even though they never get on the next ball and miss every other shot, they see it as a strange occurance that won't happen next time.
A casual player is someone who never tried to learn, can barely point the cue in the general direction of the cue ball and pretty much only plays just because the table is there or on a date. Those girls that stand almost backwards to the table and form pretzel shapes with their arms over their heads with the cue weaving around like a flower in a storm is a casual player.
Someone who never wins a game against even a C player but keeps saying they played bad and will get them next time or "that was a close game" when they made 4 balls in a race to 7 is a banger. Even a slightly accomplished player that can make shots only because they played for 10 years but does not know exactly what they are doing could be called a banger. Those are players that will make a long striaght shot and then miss a simple short shot right after or just end up with the cueball opposide side of the next shot.
That's pretty much what I was thinking...
I think that every player who learns the most basic basic stroke enough to hit the CB consistently without miscuing, and knows at least one ruleset to play the game by (let it be WSR, APA, bar rules or something else), can be called a "casual player". From that point they can start learning the game legitimately, by reading books, watching instructional pool videos, or taking instructions. That way they become regular pool players, with good fundamentals, consistent stroke and at least basic position play, who have a good perspective to learn and improve further.
OTOH, if they stick to bar rules, "teach themselves" and learn the game only from other bar players, they become bangers. They still improve simply by experience, but they never have a good consistency. Usually with unstable stroke and no position play, but some bangers with 5+ years of regular pool playing can become quite good shotmakers. Their position skills remain low or average at best, and are very inconsistent.
So, to sum everything up, I made this little chart:
Fundamentals
Casual players: bad
Inexperienced regular players: good and improving with time
Bangers: bad (they never really learn them)
Shotmaking
Casuals: bad to terrible
Regulars: average and quickly improving, due to good fundamentals
Bangers: bad to average, becomes better, even much better (with experience), but usually remains inconsistent (bad fundamentals to start with)
Position play
Casuals: non-existing
Regulars: some learn it from the start, others later, but becomes good with practice
Bangers: minimal, can improve a little with time (depending on the banger's understanding of ball movement and strategy), but also remains inconsistent
Safeties
Casuals: poor performance
Regulars: can be inconsistent at first, but improving
Bangers: usually bad, sometimes ok, but they rarely play safe to begin with
Tactics
Casuals: very poor, usually afraid of making mistakes and embarassing themselves, don't really care about winning
Regulars: learn to play with a cool head and think in advance, not risking too much and playing safe when necessary
Bangers: lower bangers - poor, "advanced" bangers - very unconventional, offensive, sometimes can surprise even better players, have courage to try almost any shot, ready to do anything to win
