The "normal" backup type is the most standard. This is the backup type that you would use if you wanted to backup every file in a given folder or drive. It backs up everything you direct it to regardless of what the archive bit says. It also resets all archive bits (puts the flags down). Most backup software, including the built-in Windows backup software, lets you select down to the individual file that you want backed up. You can also choose to backup things like the "system state".
When you schedule an incremental backup, you are in essence instructing the software to only backup files that have been changed, or files that have their flag up. After the incremental backup of that file has occurred, that flag will go back down. If you perform a normal backup on Monday, then an incremental backup on Wednesday, the only files that will be backed up are those that have changed since Monday. If on Thursday someone deletes a file by accident, in order to get it back you will have to restore the full backup from Monday, followed by the Incremental backup from Wednesday.
Differential backups are similar to incremental backups in that they only backup files with their archive bit, or flag, up. However, when a differential backup occurs it does not reset those archive bits which means, if the following day, another differential backup occurs, it will back up that file again regardless of whether that file has been changed or not.