Clauses - these are sections, much like paragraphs in an essay. Each clause typically addresses a particular topic. They are also called articles or provisions.
Stipulations - statements of the requirements and conditions imposed on parties to the contract. Stipulations are stated within clauses. Many clauses in contracts are primarily stipulations.
So, all stipulations are contained in clauses, not all clauses are stipulations.
For example, there will be one or more clauses that just state the purpose of the contract and the parties to the contract, but will not say one party is required to do something.