Use “wind up” to describe the ending of a situation:

I think if we go home now we’re just gonna wind up skipping the party.

When talking about something in the past, use "wound up":

She wound up missing her flight and had to wait five hours for the next one.

We especially use "wind up" when the ending is unusual or different from what you expected. 

“Wind up” is very similar to “end up.”

There's a good chance that you'll end up buying a lot of stuff while you're there.

“Wind up” is used for more complicated or chaotic situations.