Online: When you "sign up" you adquiere/join to a service without any compromise, generally you will only use it (of course there are some norms). Another example: you could also sign up a petition for giving it support. Online: When you "register" you join to a service but this might imply some compromises for its use as giving important personal information. Another example: you could register for being a voluntary to do some social work Best Regards, Al

They are interchangeable in conversation, but not in official documents. You'll see "sign up" very often on the web (sign up for our email list, sign up for an iTalki account, etc.) because it is more casual and conversational. Schools, businesses, and government would use "register" (register to vote, register for classes, etc.) in the same situations.

In many cases you could use either, but "register" is a bit more official or formal. If the class is having a party and you put your name on the list to bring cookies, you would "sign up". If you fill out a government form to vote in an election, you "register". If you enter your information online to do a running race, you could say either "sign up" or "register". Basically, if there is official paperwork of some kind "register" can work, but if it is just a casual circumstance, "sign up" is better.