Need Help Migrating A Site

Hello! I had a questions regarding migrating one wordpress site to another website URL. I have website X where I have everything and I want to move everything to Website Y which is a brand new site with a different site name that I want. My question is if I buy Migrator or Updraftpremium, do I need to have these installed on BOTH websites to do the migrate (meaning I’d have to buy two licenses?) or do I just need it to be on the new website? When you get let’s say Updraftpremium it is for a single site license correct? Let’s say I put this on my new website, how do I then access the migrate feature on the source site?

Again my question is do I need to have these installed on both or just one of the sites and if so, which site do I put it on? The source site or the new one where I’m migrating everything to?

Appreciate the replies!
All the best,
Alex