Alright, this bugged me the entire time I was watching Saving Private Ryan...
Their version of covering fire is getting out of cover, shooting for a while (hoping that will do some damage to the enemy) and then returning to cover, sending out men to rush the defenses. Now tell me if I'm wrong, but I think covering fire is continual fire to keep the advances covered, not finishing right before the men go...
And as for supressing fire, that's to try and kill the enemy before anything else.
Is there anything other than covering and suppressing? Please correct me if I'm wrong on either or both. That just really bugged me...(not saying I look for historical accuracy in SPR

)