What's the difference between a snare and a stun? And is one more effective than the other?

Snare / Root only makes you unable to move.

While stun makes you lose control completely.

Stun is more effective.

http://leagueoflegends.wikia.com/wiki/Types_of_Crowd_Control

How long have you been playing that you don't know the difference between two very common forms of crowd control?

There's also an Entangle, which is a special type of root caused by 's ult that also prevents autoattacking (but not spells or abilities).

What's the difference between a snare and a stun? And is one more effective than the other?

Riot decided to re-brand "Snare" into "Root" concerning tooltips and game vocabulary, as snare's definition doesn't support the way that word's been used and root gets a better idea across.

As far as which one is more powerful: roots set a unit's movement speed to 0 and silence the vast majority of mobility abilities along with Flash. In multipurpose abilities that grant mobility as part of the effect like Caitlyn's 90 caliber net, the ability isn't silenced but using that skill while rooted doesn't grant any mobility.

Stuns disable a unit from using, attacking, casting abilities, using most item actives (outside of debuff-removal abilities and debuff-removal item actives), and using mobility summoner spells. However: stuns don't disable you from using summoner spells that don't grant mobility, allowing things like Barrier, Heal, Ignite, and Exhaust to be cast mid-stun.

is one more effective than the other?

In a void stuns are more effective, though in practice stuns tend to come with much shorter durations while roots tend to come with fairly monsterous durations, leaving to several situations where spells that apply roots are more potent than spells that apply stuns.

It's also worth noting a root doesn't effect everyone the same way. If you root a champion like That guy is still capable of unleashing all his damage within a ~1,000 radius of where he was rooted, he's probably skirting the edge of a fight due to his range and rooting him doesn't put him in immediate danger if his positioning was ok before eating the root, if he's in a bad spot Zhonya's is occasional an option in that situation, his auto-attacks can still reach units within a pretty impressive circular area, and you're just not preventing him from laying down the QWER on your team by tagging him with CC. Within Zigg's QWER, he also has one of the best zonning tools in the game via his minefield, which can make getting to a rooted Ziggs extremely treacherous.

Alternatively, hit a champion like And you pretty much applied a longer-duration stun for all intents and purposes, and probably spelled her death-sentence by landing a root on her. As a squishy melee champion heavily reliant on mobility to survive, completely eradicating her mobility is extremely effective at shutting down her kit. As roots also silence mobility skills, Riven cannot cast Broken Wings or Valor, her triple-hit AoE gap-closer skill or her AD scaling HP shield gap-closer skill, while she's rooted. As a melee champion roots also prevent Riven from striking anything that isn't adjacent to her, which should be nothing if her opponent's aren't potatoes. And as a high-risk, high-reward melee champion: Riven should be in a dangerous spot when she's tagged with a root: allowing her opponents to collapse on her.

Generally speaking: Roots are better than stuns vs. a wide range of speedy and mobile champions heavily reliant on speed to survive, and roots are solid vs. pretty much every melee champion. You just have to hit them with the skill first (not to hard in the case of roots, as they generally have the width of a schoolbus).

Anyways: because of the way Riot balanced out stun and root skills, neither is really better than the other in a wide range of circumstances, though stuns are better if they have the same duration and delivery system.

if people are snared they can still auto and use all of their spells. if they are stunned they are unable to do anything.

Snare inhibits movement and movement-related abilities only. You can still do everything else. Morgana Q is a famous snare.

Stuns inhibit movement, movement-related abilities, and auto attacks. You can still use most summoner spells (not flash, because it's movement related).

If you're interested, here's some more info/trivia:

• Amumu's bandage is a stun, but his ultimate is an "entanglement", which is a root that also prevents auto attacking
• Snares will not interrupt channeling abilities, but stuns will
• Neither stun nor snare stops most summoner spells, so stunning the jungler won't help win a smite battle unless he's out of range
• Knockups are part stun, part snare. If you qss them, you can cleanse the stun part, which will allow you to use abilities but not move
• Suppressions are the only cc that will restrict all your summoner spells, and the only way to remove them is a QSS. WW ult, Malz ult, Urgot ult, and Tahm eat are suppressions.