I know that the employer is required to make up the difference if the employee did not make minimum wage.

A recent situation with one of my employees:

For two consecutive days, the waitress made $7 in tips during a 6 hours shift each day- (so $14 in tips for 12 hours of work) because of slow business. The employer told the waitress that they are only required to pay them the difference if it did not 'average' out over the 2 weeks pay period . . . is this true?

I hope I explained that so you can understand . . .

Basically the employer told the waitress that on Friday night she made $80, which more than made up for her 'two bad days'.

No, it's not pay period, it's by workweek. All FLSA requirements look at the workweek, not the pay frequency.

But, if it averages out over the workweek, that is compliant.