“Sign up” refers to the website requiring a digital signature in accordance to the terms and conditions of an agreement. Sign is just a short form for signature. Providing and verifying an email address could be considered a signature, if that is stated in the conditions.
“Create An Account” is what you do after you have signed up. An account needs to be associated with a signature or profile, and often that can’t be done until a visitor completes the registration process. That registration process may required them to agree to terms and conditions (that’s the sign up part).
If you do not have any terms or conditions, then you just want them to register.
It’s possible to allow a visitor to create an account without a registration process. Websites that offer anonymous services for example, and link the associated account with a profile threw visitor tracking methods.
“Log In” refers to the action of recording your entry into a security log. It implies that the activity will be recorded. Where as, the term “Sign In” refers to the action of authenticating a signature.
These are all old computer terms that have been so incorrectly used so many times on different websites.