Circuit breakers, unlike many fuses, have a time delay curve on them. A significant overload will trip them fairly fast, a load slightly over their limit can take some time before it trips. Starting both units at the same time could cause enough surge to trip it. Your supply voltage is unlikely to be always the same. 120vac nominal at 20A= 2400W, but if it was say 110vac*20A = 2200W...so in one situation, it wouldn't be overloaded, but in the other, it would.
Without knowing the supply voltage, in both cases, you're close to the maximum and may exceed it sometimes. If there's anything else on the circuit, that can easily push it over the edge. That type of appliance typically isn't used continuously, but if they were, there's an 80% rule, and in all cases, you'd be overloaded. That generally only applies to something expected to be on continuously for a long time.