Lenders on PPP applications call these "Entity types" without further defining this term. However, best to my knowledge:
Sole proprietor is someone who owns 100% of business and files Schedule C together with 1040 form. This choice relates to Tax Filing Status with IRS.
Partnership is when multiple people own business in equal amounts and file form 1065. This choice relates to Tax Filing status with IRS
Independent contractor is someone who could be either Sole proprietor or Partnership. But focuses mostly on B2B work that implies that Independent Contractor is receiving 1099-MISC form from his clients as transactions are with other businesses (Opposed to B2C type of work where businesses are not getting 1099-MISC form from clients that are consumers). This choice relates to transaction types.
Self-employed is someone who owns and runs his own business - in other words anyone who is not employee. This could either be partnership or sole proprietorship. This choice relates to work management type.
It seems that answers from different classes are mixed together hence there are multiple correct answers.