What is the difference between certificate, degree, course record and diploma? (PhD application documents)?

I would assume that the program wants you to document that you have completed an undergraduate degree and/or masters. Usually sending in your transcripts will suffice as this will show all course work you have completed, your GPA in theses courses and degrees completed. In some fields, you can/need to be certified to before you can work. Just because you have a degree doesn’t mean you are certified. Showing proof of you certificate would show that you are certified. I have not heard of having to send in your diploma for application to a Ph.D program. Usually your transcripts are enough. I am not familar with every program or field so maybe some do require this.