Is there any difference on backup process whether it is recovery model is Full or Simple?
A full database backup will give you everything in the database regardless of recovery model.  Upon restore, any transactions that were still in-flight when the backup completed will be undone.

Recovery model really comes into play during restores.  

With SIMPLE recovery, you can only take full and differential backups and that is the granularity that you can restore.

With FULL recover, you still take full (and optional differential) backups, but you also take transaction log backups and can use the combination of the full, diffs and logs to restore to a point in time.