When asked to select the employer type on your 1042-S/W-2 form, you have to choose the answer closest to where your income is coming from.
For example if you income is from a university/college and you had a scholarship or a part-time job there, you should select 'College, University or Other Educational Institution'. If the income is from employment, for example an Internship or a full-time job, you should select 'Company'.