Wrist computer VS manifold is are not in the same category to compare.
Manifold usually refers to the crossbar connecting two tanks to form a set of doubles.
Computers & gauges can come in wrist and console varieties.
Computers are electronic with computer algorithms. Gauges can be analog or electronic, but don't use algorithms. They just list what they're supposed to without calculations into nitrogen loading. Some computers can be set into a gauge mode.
The debate between having an analog pressure gauge VS an Air integrated has been brought up many times here. Try a googling
site:scubaboard.com backup SPG AI
Or something along those lines
Since you're confusing terms, I think it would be best to wait for your certification class to start and even then wait until the topic has been discussed in class. A lot of this will be discussed and defined in your class. Just be patient for the class to start if you're still confused right now.
We could explain these things to you in depth but in doing so would have to define new terms you may or may not have heard before. It would do your instructor a disservice if we did his or her job. After each class if you still have questions, then feel free to ask your instructor and post a question here on the board.