Do different formes learn different moves?

Question

Like shaymin sky form or mow rotom or trash wormadam

Answer 1

Here are all the ones I could find:

Shaymin Sky form learns:

• Quick Attack (instead of Synthesis)
• Air Slash (instead of Aromatherapy)
• Leaf Storm (instead of Healing Wish)
• Air Cutter, Ominous Wind & Tailwind (instead of Earth Power & Endeavor) by move tutor

Rotom learns a special move when it changes form:

• Mow form: Leaf Storm
• Fan form: Air Slash
• Wash form: Hydro Pump
• Heat form: Overheat
• Frost form: Blizzard

Wormadam learns a few different moves by level up, move tutor and different TMs. Below are the level up differences, go to the Wormadam pokedex to see all the other differences because there are a lot.

• Plant cloak: Razor Leaf, Growth & Leaf Storm
• Sandy cloak: Rock Blast, Harden & Fissure
• Trash cloak: Mirror Shot, Metal Sound & Iron Head

Deoxys learns some different level up moves:

• Normal: Knock Off, Snatch, Recover
• Attack: Taunt, Superpower, Zap Cannon
• Defense: Spikes, Counter, Mirror Coat
• Speed: Double Team, Swift, Agility, Extremespeed

Giratina and Arceus have the same moves regardless of form.

Answer 2

Yes.

Sky Shaymin: Quick Attack, Air Slash, Leaf Storm

For Rotoms, see this question.

I'm not sure about all attacks of Wormadams, but I'm sure that they learn different moves.