Well!
1) Sorcerers could have distinct casting mechanics from Wizards.
Different spell lists with minimal overlap would be HUGE for creating some light between the two. Giving the Sorcerers a Spell Point system with their 'Sorcery Points' for Metamagic folded into that would go a long, LONG, way to making them feel different. Give them spell point per round expenditure limits, recovery mechanics for some portion of their spell points at the end of short rests, etc.
Maybe give them the ability to specifically burn their Hit Dice to recover Spell Points to represent them using their very body as fuel for their magic. Hell, give them the ability to do that as a bonus action when they're out of spell points but they also take damage equal to the spell points gained.
Since they're all so charming, build in some charm/distraction/social mechanics into the class that allow them to manipulate people in a pseudo-magical way.
2) Wizards could be built around Knowing Things.
Not just the "Scholar" function granting extra skill proficiency. But build up some Wizard-Specific DCs to recognize NPC vulnerabilities due to their various studies. How about a mechanic which allows them to mark a specific target for the rest of the party to gain some bonus to attacking or rolling saves or whatever else exists against that ONE GUY. And it's based on a Relevant Knowledge Check with a DC of 10+Proficiency+Cha mod of the target or something similar. Or 10+Deception Mod or something.
Give 'em some abilities related to finding information on characters, quests, and objects through Research or finding weird Academics, Philosophers, or even Conspiracy Theorists to ask them for information.
3) Psions could be built around Vibes and Dice.
Ever heard of Psychometry? It's Object Reading. Make that a class ability for them to touch some ritual dagger and know exactly who it has been used on. Or talk to the "Ghosts" that hang out around people like some Spiritualist doing seances. Allow them to use Insight instead of Investigation to represent them "Feeling what has happened, here" to add to that identity.
Give them dice they roll as part of their casting mechanic either to try and preserve their power or boost it with direct modifiers that get lost or kept after use, depending on the roll. Or structure their powers as Cantrips and give them spell points they can spend to boost those cantrips in various ways like increasing the damage from 1d8 to 3d8 to make the cantrip deal as much damage as a 1st level spell if they spend the number of points required to do so. You could make -all- their casting "Buffed Cantrips" that way and free up lots of space for other aspects of the character class.
Frankly, there's a TON of really great options, out there, to make them all feel different, even if they're just moving and casting a spell.