The word, "video," is often included when using the words, "footage" and "clip."
"Video footage" often indicates that something has been recorded, like a security camera recording a thief robbing a store. The police would ask the store owner, "Do you have any video footage from the robbery?" "Video footage" is usually used in terms of proof via video.
However, it may also be used to describe a section of an entire video, or describe an entire video itself. For example, "I wasn't able to attend their wedding, but looking at the footage that their videographer had taken, their wedding looked like a lot of fun!" This indicates that the person watched small portions from the couple's wedding video. Had the person watched the entire thing, he would have said, "but <em>having watched </em>the footage...."
"video clip" is used normally for online activity where short videos are called "clips."
For example, "I watched that clip of you doing a cartwheel." or "I watched that video clip where you did a cartwheel." In this instance, just saying "clip" conveys a non-specific meaning, whereas, when you say "video clip" this means that you are referring to a specific short video.