What are acceptable “relationships with referees”?
Assuming that you mean "references", they should be people who know your academic work well. Basically anyone is acceptable as long as they can be expected to give a fair and accurate statement about what you have done and about your probable likelihood of success in the academic program. 

Professors, advisors, employers, Lab PIs. etc. are all fine. They need not be supervisors, but can be. Your mom, and uncles, however, aren't the best, nor is a spouse or child. Anyone with whom you have had a professional/academic relationship and has some stature is a good choice. 

As for the description, just say it like it is.