Size of circuit breakers for 220v circuit
They are the same thing and you don't have a choice.   Your breaker is going to be a 2-pole breaker rated 15A.  When you look closely, it will very much resemble two 15A breakers bolted together.  That's not far from the truth. 

The breaker will mount in the service panel in two spaces, which could otherwise accommodate two 120V breakers.  What is happening is there are two 120V buses in the panel, and the 2-pole breaker is designed to tap both of them.  They are phased opposite (when one is -120V the other is +120V), so if you tap both, you get 240V.