Is every AVL tree a BST or just BT?
Yes every AVL tree is a BST

also note that every binary search tree itself is a binary tree (binary tree is basically a tree that each node has at most two child)  so therefore every AVL is a binary tree as well.

AVL tree is just a binary search tree that tries to do rotations when its needed (when the tree becomes unbalanced) in order to stay balanced, and therefore the search time would be O(logn)

the reason behind using AVL instead of BST is to make sure the search time is O(logn) because if we use BST and insert the values in a decreasing or increasing order then the BST would be one sided and the search time will be O(n), but if we do that using AVL then the tree will balance itself using rotations. 

i suggest you to read the definitions of all of them so you can understand better.