Is a balanced binary tree a complete binary tree?
A complete binary tree is a binary tree of length $h$ such that all the levels from $1$ to $h-1$ are completed and the last level gets completed from left to right. As in the image below.

A balanced binary tree is a binary tree of height $h$ such that the height of any node’s right subtree and left subtree differ no more than $1$. So it doesn't say anything about it having to be completed from left to right.

The figure above describes this trees very clearly in a recursive way.