I think it's worth just in future getting to know someone well before being too keen.
Some people respond well to it, others not so much - that's just part of us being different and human - some people aren't going to accept you exactly as you are, for me I wouldn't try to hard for that acceptance and would just decide we aren't compatible - you do seem to want to have that acceptance to help with your sons friendships so that is where you would need to get to know them and adapt to their personality style in terms of how often to contact/enthusiasm etc.
E.g. mum 1 is a single mum who's a little lonely and loves the enthusiasm and really wants to make a friendship whilst the kids play - enthusiasm welcome.
Mum 2 has a busy hectic life, some medical issues, a full friendship group and lots of family commitments
Mum 2 may be an every other month at most play dater and feel a bit overwhelmed if asked too often - doesn't mean you've done anything wrong it's just not so compatible
A lot of it is reading between the lines when you communicate - if they don't contact first/ask you first, or ever talk about things other than keeping it light/about the kids, then I'd leave it a couple months before asking for another play date - or not at all and offer when they're older and can be without parent to spend time together.
Same with the word crush, talking about boyfriend/girlfriends etc. my boy had a good friend between 18months and 3 years and the mum would call them boyfriend and girlfriend as a joke. I wasn't massively keen as it's just not part of my mindset/culture to think of it like that. It didn't bother me enough to distance - as I'd been friends with the mum about 10 years - if it had been a new contact perhaps it would have done. Better to avoid the language unless you know the person and know that's language they use - as it won't be to everyone's taste. It isn't particularly offensive I don't think, just some parents won't want a young child referred to as a crush/boyfriend etc.
I don't think you did anything wrong - it works with other friends you have, just didn't with this one. And your son and her will still play happily at nursery, just part of life that some friends are just in school/nursery - others are outside as well.
I am sure you will make more contacts once he is in school and there will be more play dates. Keep it casual and enjoy :) bear in mind some parents don't want to get too close to other parents in case the kids fall out - and see it all as just light chit chat and casual encounters mostly rather than 'friendships' and I think you'll go fine