OK, here's how it works:
When you have toe straps, you use toe clips. You use clips and straps when you are using pedals that require/can accept clips and straps. I suppose people could use just straps, but that seems stupid. Using clip/strap pedals without toe clips does not equal clipless. Using clip/strap pedals with just clips is just stupid. Clips and straps are a system meant to go together. Don't use straps without clips.
Clipless pedals are pedal systems that do not require toe clips. Those are the ones that have the cleat on the shoe that locks onto the pedal.