Hey Artem, First of all, go ukraine 🇺🇦 And secondly, mental state usually refers to a temporary state. For example you can many mental states throughout the day in the morning you’re very relaxed and then something frustrating can happen at work and you can be in an angry mental state( you won’t ever need a doctor to help decide your mental state). Psychological state refers more about your long term mental status. Like someone is depressed or someone is dealing with an anxiety condition or post traumatic stress disorder, or even a more serious mental condition, a doctor might help determine your psychological state. Let me know if this makes sense :) Also, this is just a native speakers opinion and how people in my area would interpret that. :)

As a native speaker, they are basically the same. You can use both. A professor may have an opinion about a small difference in meaning, but in normal conversation these two forms are understood in the same way. Good luck!

A mental state, or a mental property, is a state of mind of a person. Mental states comprise a diverse class including perception, pain experience, belief, desire, intention, emotion, and memory. Psychological state - (psychology) a mental condition in which the qualities of a state are relatively constant even though the state itself may be dynamic; "a manic state" mental condition, mental state, psychological condition. cognitive state, state of mind - the state of a person's cognitive processes. MUCH LOVE