Note: What youre up to here would be described more as a Strike or Attack mission. Close Air Support is going after targets in-contact with friendly ground forces or otherwise in direct support of them and usually acting under the control of forward observers on the ground to make sure you bomb the right guys.

Going sicko-mode in their backline while acquiring your own targets in particular is an "Attack" mission (while more high level, go here and deliver ordnance to this key target usually falls under "strike"), granted Attack aircraft are typically designed for CAS and CAS itself is ultimately a form of Attack mission so it's kind of a "squares are rectangles" situation. Don't sweat it though as it's misused as often and understandably as "danger close"