The Mentalist was a more serious version of Monk. I think that the connection between Psych and The Mentalist is tenuous (despite the references in Psych). As for the connection between Monk and The Mentalist, here are the character comparisons…
Patrick = Monk (the main man loses his wife to a killer who takes seasons to be caught*).
Cho = Leyland (the straight-faced detective).
Rigsby = Randy (the dim-witted sidekick).
Lisbon = Natalie (the main assistant).
Van Pelt = Sharona (the lesser assistant who eventually dates the dim-witted sidekick).
Both TV serials have an episode involving a parachute blunder. Both TV serials have an episode where the detective is blind. I won’t tell you which episodes because it would spoil the surprise. Still, fans of The Mentalist can hardly say that the blind connection was a coincidence. As for the M connection, these TV serials are the ultimate murder mysteries whose content is embodied by the M in the titles.
The makers of Psych seem to think that The Mentalist is an imitation. However, The Mentalist was about someone who previously pretended to be psychic. To the credit of those behind Psych, The Mentalist had an episode about an Old West tourist attraction.
As for the pictured characters, Psych and Monk have episodes about murdered food critics. As for other similarities, there are episodes about retirement homes, fake aliens, daredevils and murdered models. After Psych came to an end, people wished that there could be a TV movie which allows a Monk crossover.
* Intriguingly, this is the same premise as Life and Endgame.