Is cover letter another name for the statement of purpose for a PhD position? US Universities typically ask for a formal "Statement of Purpose" while European universities have no such specific requirement. Instead, most of the times they ask for a cover letter. I've been told that cover letters should describe what you have done, what you are currently doing and your future plans. They should also be personalized to the university you are applying to. The description looks similar to the statement of purpose.

Are they both the same thing? If no, what are the differences?
Short answer: Between academia and industry they differ in usage, but amount to the same thing between academic institutions.


  I've been told that cover letters should describe what you have done, what you are currently doing and your future plans. They should also be personalized to the university you are applying to.


This is basically true. A professional cover letter follows what amounts to a three-section format: 

1) What is the position at company X, where did you see the listing, and why does the position interest you?

2) What qualifies you for the position? Without rehashing your resume/CV, give mention to what it is you've actively done at your previous positions in an effort to draw attention to your resume.

3) This is where things differ: In a professional cover letter, the last section is where you want set up a workflow that allows the hiring company to follow up with you should they wish to contact you. They aren't really interested in your future plans, and I've seen applications that, for example, want you to list faculty you want to work with and why in your academic SOP... there's no room for any of that in a professional cover letter.

So it's essentially the same, with some difference because of the difference in audience.

Between the terms being interchangeably used between academic institutions, however, they amount to the same thing.