“Over the wicket” and “round the wicket” are not literal descriptions but simply indicate which side of the wicket (at the non-striker’s end) the bowler runs when bowling.
“Over the wicket” means the bowler’s arm is between their body and the wicket. “Round the wicket” means the bowler’s body is between their arm and the wicket. (Which side of the wicket this is will depend on whether the bowler is left or right handed.)
Bowling over the wicket is the more common option when the bowler and batter are both right-handed (or both left-handed), particularly with a fast or medium bowler. That’s because the angle the ball will travel makes it more likely the batter will be bowled, caught or LBW. It’s much harder to keep all three of these as strong possibilities when bowling round the wicket.
Bowling round the wicket tends to be used in more specific cases such as:
a right-handed bowler facing a left-handed bowler (or vice versa);
a poor batter who is unusually vulnerable to being bowled;
a bowler who is much more concerned with avoiding conceding runs than taking a wicket;
a less experienced batter who is not used to facing bowling around the wicket.
The Laws of Cricket say the bowler must tell the umpire which arm they plan to use and whether they’ll bowl over or round the wicket. The umpire will then tell the batters. The bowler must tell the umpire before changing either the arm they use or the position they bowl from; if they don’t, the delivery will be called a no ball.
The non-striking batter also needs to know which method the bowler is using. This allows them to stand on the other side of the wicket so that they don’t block the bowler’s run-up or the batter’s view.
Despite the name, bowlers don’t usually get close enough that they literally bowl over the wicket. This would risk accidentally knocking the stumps with the foot or hip and knocking the bails off this way would mean a no-ball.