What's the difference between approaching a girl and hitting on a girl? How can I make a girl think I'm approaching her rather than hitting on her?

approaching a girl is meeting a girl, it consists of walking up to someone

hitting on someone is one way or another expressing your sexual intentions towards someone either through validation or some other means, different people will have different ideas of what this means
just have a reason that can justify your approach that is unrelated to a romantic pursuit

for the most part though a good question to ask yourself if why would you want to do this? what benefit are you hoping to achieve by hiding that you are attracted to someone that you ultimately have a romantic interest in?

if you hope to pursue someone that interest you, you will ultimately have to express your intentions at some point regardless

Same as what pump said approaching can be done to anyone it's just a means of initiating interaction with a person while hitting on means you're attracted to the girl and want more than just a regular conversation.