Since I was only dating this girl for only six weeks and she decided to end things wouldn’t this be more of just ending things as opposed to a break up? It felt more like 6 months.

It's all just a title. There is no definition. Call it whatever you like.

Both produce the same results regardless of how you word them.

There is no difference.

It's the difference in what you feel more comfortable with saying

Are you together or apart?

They're just words, the outcome is the same.