The pitching designations represent how you, the manager, would like that pitcher to be used, which may or may not matchup to how the pitcher was used in real life that particular season. Here are the general guidelines:
The A/B designation is an additional control for setting pitcher usage. An A designation will almost always be used before a B designation of the same role, e.g. if you have one pitcher set to Setup A and another set to Setup B, the Setup A would receive priority in a setup situation. If both pitchers are set to A, then the SimManager will decide who to use based on the situation (opposing righties/lefties, pitcher fatigue, etc.).
Each of these roles work with your Player Settings to determine actual usage, primarily the "Min Inning Available" setting. A typical scenario would be Mopup can enter in any inning, Long Relief in 4th or higher, Setup in 6th or higher and Closer in 8th or higher. But that's where you come in and can specify ideal usage.
*** Please note that if you don't designate a pitcher for a specific role, you may be sending the wrong (or right) message to the SimManager. For example, if you put all of your bullpen pitchers on rest, that would be an indication to the SimManager to leave the starter in as long as possible, regardless of his call bullpen and pinch-hitting settings. Another example might be setting all of your pitchers to rest except for a closer. This would indicate to the SimManager to leave the starter in until a save situation arises. If the starter is getting shelled in the 5th inning, the SimManager would leave him out there rather than use a closer in the 5th inning. It's recommended to have at least 1 pitcher set for each role. Not having a pitcher available at a specific role may have undesired results.