OP:
A peculiarity of the code is that 15A and 20A outlets may be used on 20A circuits. For this, the two types have identical quality and current capacities. Meaning there’s no point in putting in a 20A outlet in a 15A circuit, it’s not built better. Some makers even use EXACTLY the same conductors in both models, but different face plates to save money.
The theory here is that some circuits, like the kitchen counter, may need a 20A circuit to handle multiple appliances at the same time without nuisance tripping. So the circuit is 20A, but each outlet may have a 15A face plate. The outlets still have to be safe to use on the 20A circuit, so the construction is always the same. 15A outlets do not have thinner conductors.
However, no, you should not put a 20A plug on a 15A outlet as the T shaped hot pin indicates it is safe to use for 20A devices, like industrial vacuum cleaners.