Typically I click 注册 = "register" to sign up for a new service on my phone. However, 登记 also seems to mean "register" in a similar sense. Searching on Jukuu.com:
Marriage without registration is not recognized by law.
Elementary school enrolment begins tomorrow.
They seem similar, but I don't think they're interchangeable. I'm not clear on this.
Question: What's the difference between 注册 and 登记?
(Note: The relevant question What are the differences between 报名，登记，挂号？ doesn't cover 注册)