Żeby and Aby, versus in polish

What's the difference between Żeby and Aby?
Żeby mieć konia to trzeba.....
Aby mieć konia to trzeba....

The meaning to me sounds the same, yet I want to know when to use what word and why.

Also what's the Polish equivalent for the English vs(versus).
Thanks

versus = kontra or przeciw.

żeby = aby in most cases, but sometimes you can't use them interchangeably. Look at the example below :

żeby nie Tomasz, nie wydostalibyśmy się = hadn't it been for Thomas, we wouldn't have escaped. In this example, you can't use aby.

Generally, we use aby and żeby interchangeably if they mean "in order to"; "so that"

I always use aby (in the meaning of "to/in order to"), because I'm afraid that I may misspell żeby and make "żaby" of it (żaby = frogs) and no word editor would correct that for me :)

I'm not sure I'd agree.
"zeby" does not sound right here. It should be:

"gdyby nie Tomasz..."