My daughter did an internship and was paid without taxes but it keeps asking about owning a business

If her earnings were reported to her in Box 7of a 1099-MISC, instead of on a W-2. then the income is considered "self-employment" income, and is reported as business income on Schedule C of her tax return.  In that situation, she is considered the "owner" of her own business.

An employee's earnings are reported on a W-2.

In addition to income reported in box 7 of a 1099-Misc, the IRS considers undocumented cash income (no W-2 or 1099-MISC), for work performed, to be self employment income.