Exegesis and exposition are like making a cake. Exegesis is the eggs, the flour, and milk -- plus all the tools that you use. Exposition is the final product. You leave your exegesis in the kitchen (study) and bring the finished cake (exposition) to the table (pulpit).
For instance, I will do a structural analysis of the passage in Greek ... for MY benefit, but I will never mention it in the pulpit. I will do word studies, but never mention a Greek word from the pulpit. There are many things that go into the sermon that build it and make it and form it, but should never make it into the pulpit. In other words, exposition is the fruit of the exegesis.