tl;dr -> If you don't know that level of mastery, you just don't get the boosts that come from having that level of mastery. Each character's mastery only applies to that character.


Long version, since I've already typed it:
The levels of mastery (Expert, Master, Grand Master) provide additional bonuses when a character acquires that level of mastery, and these bonuses either stack (if not the same) or overwrite the weaker perk (if the bonus is a stronger version of the previous bonus). Each class has its own list of which skills it can learn and what levels of mastery can be reached in each skill. Master and Grand Master may have extra requirements besides just raw skill ranks, like requiring completing a quest or having a minimum value in a stat.

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Let's look at the Bow skill as an example.
Dragon: Can't learn the skill, so a dragon can't even equip a bow (we're ignoring the fact that a dragon's basic attack is better than any bow for purposes of this discussion).

Every class except Knight, Minotaur, and Dark Elf: Can learn the Bow skill, but they can't reach Expert in it. Only the Normal tier ability applies for these classes, so they get +1 bonus to hit for each skill rank. If you get them to Bow 10, then they get +10 to hit, and that is all.

Knight, Minotaur: Can reach Expert in the Bow skill. Until they have Expert training, they get +1 to hit per skill rank, so Bow 10 means they get +10 to hit. However, when they purchase Expert training, they also receive the Expert perk from that point forward. Bow 10 expert means they get +10 to hit AND -10 bonus to recovery after shooting an arrow.

Dark Elf: Can reach Master. When they have purchased Master training, their Bow 10 gives them +10 to hit, -10 bonus to recovery speed, and they fire 2 arrows with every bow attack. If they reach Bow 30, they get +30 to hit, -30 bonus to recovery, and fire two arrows with every attack.

Dark Elf Patriarch: Can reach GM. After they purchase GM training, their Bow 10 gives them +10 to hit, -10 bonus to recovery, they fire 2 arrows each time they use the bow, and they get +10 bonus to damage per arrow.
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Let's look at spell casting. The particular brand of magic doesn't matter for our broad use case, but I'll list Air spells as my example spells.

Don't know the skill: You can't learn or use spells of this magic school.

Normal mastery: You can learn only the Normal level spells of this school. (Wizard Eye, Feather Fall, Sparks, Air Resistance)
All spells of this magic are cast at their Normal level. (Feather Fall lasts 5 minutes per skill point)

Expert: You can also learn the Expert tier of spells. (can add Normal tier spells, and also add Jump, Shield, Lightning Bolt)
All spells of this magic are cast at their Expert level (Feather Fall lasts 10 minutes per skill point)

Master: You can also learn the Master tier of spells. (Invisibility, Implosion, Fly)
All spells of this magic are cast at their Master level (Feather Fall lasts 1 hour per skill point)

Grand Master: You can also learn the Grand Master tier of spells. (All Air magic spells can be learned, including Starburst)
All spells of this magic are cast at their Grand Master level (Feather Fall lasts 1 hour per skill point and it has a faster recovery time after casting)

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Your skill points are effectively limited, so you'll only want to invest in the skills a character will actually use and use well. I would never spend points on Bow for a Cleric because they'll never reach Expert with it. I'd push a Knight to Bow 4 so he can learn Expert, and I'd stop there. Only one character in my party will increase their skill in Disarm Trap because only character can open a given chest for the first time (setting off the trap or disarming it). If I have a Vampire and a Cleric, I'll take the Vamp to Master in the Self magics (Body, Mind, Spirit), while the Cleric goes to Grand Master Self magics; the Vamp can cast (weaker) healing spells if needed and they can cast the status removal spells if the Cleric is incapacitated. All my spell casters get Meditation boosted to the max mastery they can reach.

Finally, consider what each class is going to do long term, and figure out what skill(s) will be the "dump" for all skill points earned after you've gotten everything else where you want it. For example, once my Troll has GM Mace, GM Leather, GM Body Building, GM Regeneration, M Armsmaster, and maybe M Repair Item (if a Knight isn't in my party and I don't feel like abusing the Adventurer's Guild), then all further skill points my Troll earns will go straight into Mace to increase the Paralyze chance.

My Necromancer/Lich is going to use Dark magic as his skill point dump. Cleric uses Light magic. Dark Elf is probably dumping into Dark Elf magic to boost Darkfire Bolt. Vampire dumps into Dagger, Minotaur into Axe, etc.