Here is some clarification.
You have to always start with a FULL backup. Once you have done at least one of full backup you really do not need to ever do a full backup again, but this is not a good practice.
Once you have completed a FULL backup you can then do either DIFFERENTIAL or TRANSACTION LOG backups. Again transaction log backups can only be issued if the database is in FULL or BULK-LOGGED recovery.
The key here is the restore process. To minimize the number of files to restore you can do the following.
Restore the FULL backup in no recovery mode, restore the latest DIFFERENTIAL backup in no recovery mode and then restore all of your TRANSACTION LOG backups that were taken after the last DIFFERENTIAL.
So if you are issuing both differential and transaction log backups it is the restore process that is really going to get the benefit. The differential backups really just help by cutting down the number of restores you need to do.
Another way you could restore your database even if you are using differential backups is to restore the FULL backup and all of the transaction log backups that have occured after the FULL backup.