I guess theres not a real difference, I just feel more comfortable giving her my number vs the other way around.
As far as her wanting her to text me goes, that way i'll know she's sorta interested. I been having bad luck lately.
Giving numbers either way is meant as an endgame. Not a way to gauge interest. Text to get coffee, date, sex, or meet up. Once you are in text mode, you lose the ability to read her face and are guessing her interest.
The approach anxiety you have isn't going to be alleviated by giving her your number. Say you give her your number on Wednesday, she doesn't have any incentive to call you Thursday, Friday, Saturday, or Sunday. You'll just end up feeding your anxiety.
Here is a way to help with the anxiety
Make plans for yourself, going to a movie, play, festival or whatever. Assuming you know more about her than her name, if it's something she might enjoy then give her your number so you can link up(don't chicken out and say "if you wanna or if you're free). Just tell her your plans and if she sounds excited by the idea of the event then give you a heads up on Thursday.
If she doesn't then go and enjoy yourself and talk to other women at the event. If she text you then yeah.