Hey!
Generally men’s shoes and women’s shoes are sized differently- I wear a women’s size 10 shoe, but in a men’s, I would be around an 8. However, I find women’s shoes to be narrower (which is also a size that you can look for, it’s usually in A, B, or C and they make women’s in a narrower size than men’s).
When it comes to heels, it can be a little difficult. All shoes, much like most clothing or bras, are made a little differently, so trying them on would be fairly important! Sometimes, heels can fit a little small and stretch out depending on what they’re made of, or they can fit a little large. Sometimes, they just fit small. It’s hard to know! If you’re buying online, many people will leave comments about how “true to size” things are, so look to that.
Heels also fit differently because they are shaped differently. More of your weight will feel like it’s moving forward into your toes (this takes a while to balance out, but bringing more of your weight to your heel, other than when dancing, is going to be better for your feet!), so they shoe may feel tighter because of this. Depending on the type of shoe, it can feel really uncomfortable having your toes crammed into little spaces for a while!
Not sure why your boots would say “Large,” kind of like having a bra that says “large,” it’s not a very helpful measurement!
Personally, for your first heels, maybe try some nice pumps with a bit of a platform in the toe (like, less than an inch) and see what you think! I found normally shoes with a slight platform to be much easier to walk in.
Pole shoes, however… it’s like walking in stilts! They can take a lot of time to get used to.
Good luck! Hope this helps!