It depends.
Typically, if you earn income from activities as a sole proprietor or independent contractor for which you control your schedule, clients, or overall operations in which you intend to make a profit, you would be considered to be self-employed. Please see this resource from the IRS as well as does a 1099-NEC or 1099-MISC mean I'm self-employed for more details.
If the income is from activities that are not consistent like a prize or lawsuit settlement, then it would not be considered self-employment income and would not be subject to self-employment taxes.