About the definition of a balanced tree
You're right – a single tree cannot be balanced, or rather, is trivially balanced. A collection of trees can, however, be balanced meaningfully: there exists a constant $M$ such that all trees in it have height at most $M\log n$, where $n$ is the number of elements in the tree.

For example, take any algorithm that uses a binary tree. We know that operations on binary tree take time $O(h)$, where $h$ is the height of the tree. Suppose now that the algorithm maintains the property that the tree is balanced; that is, the set of all trees that occur in all executions of the algorithm forms a collection of balanced trees. Then we can bound the running time of operations on the tree at a certain point in time by $O(\log n)$, where $n$ is the number of elements in the tree at that point.

In practice, we "misuse notation" by calling a single tree balanced. What we mean that the set of all "instances" of the tree are balanced. Usually what set is meant is clear from context.