In Essence, Yes.
If you were to take the most popular species of Bonsai Which are Junipers and Black Pines you could easily grow them into big wild trees. Keeping them small and controlling the growth is all part of the skill in Bonsai.
When creating a tree the first stage we go through is Development. This is where we grow the tree to thicken the trunk and the first branches. This is usually done in nursery pots or in the ground. By allowing the tree to act natural it will thicken up over time.
Once we are happy with the thickness of the trunk we can then start going into our Refinement stage. This is usually where the tree will find its home in a Bonsai Pot.
In this stage we are looking to stunt the trees growth now by restricting the root system. By putting it in a small pot what we get is smaller finer root growth and in return we get smaller finer growth on the top of the tree as well.
So in short yes a Bonsai is just a little tree, but its not little by nature it is little by Design.