Sneak is much different than stealth. Everyone can sneak but only the nightblade can stealth. Sneak attack provides bonus damage when attacking with a weapon (stamina based, concealed weapon is magicka and doesn't benefit nor do any staff heavy attacks). When you are in combat you are no longer able to sneak. You can hit cloak and go into stealth but sneak attack's bonus damage is unavailable until you can get your eye to close and enter sneak.

PVP sneak is a little tricky, you can be in combat due to group member putting you there and still enter/stay in sneak. Generally, you can always enter sneak if you kill any targets you've done damage to. So if you sneak attack someone and kill them you can enter sneak right away, if you steel tornado a group you wont be able to enter combat for some time or until the group is dead. Sneak attack in pvp was nerfed I believe when 1.5 came out so I wouldn't expect much more damage than just getting a crit.

Since release doing both cloak and stealth before attack results in significantly higher damage than either of the two separately. So WAI...

SNEAK CRIT

-crouch and gain HIDDEN status
-huge damage bonus to physical attacks
-physical attacks are stamina-using attacks that do Physical Damage (and possibly some Magicka using attacks that do Physical Damage)
-includes standard light/heavy attacks with regular weapons
-most, if not all, Magic Damage attacks WILL NOT SNEAK CRIT; crouch to gain HIDDEN status and then Magic Damage attack will not even provide a REGULAR CRIT

REGULAR CRIT

-can happen randomly while using skills or light/heavy attacks, or by the cloak morph that guarantees a CRIT
-this is any regular crit attack, as all attacks go off your % to crit
-much less damage than SNEAK CRIT, and is a separate thing entirely
-magic crit and physical crit % are different, depending on your character

CLOAK

-does not in and of itself increase damage
-cloak only increases damage indirectly by 1) keeping your HIDDEN status locked in or 2) the morph that guarantees a REGULAR CRIT on your next attack

Sample results from testing I performed after 1.6:

1. Veiled Strike unmorphed from HIDDEN: 1000 Magic Damage (No crit of any kind occurs)
2. Cloak morphed to guarantee CRIT -> unmorphed Veiled Strike: CRIT Veiled Strike - 1300 Magic Damage
3. Veiled Strike morphed to Stamina from HIDDEN: SNEAK CRIT Veiled Strike - 1700 Physical Damage
4. Cloak morphed to guarantee CRIT -> Veiled Strike morphed to Stamina: CRIT Veiled Strike - 1300 Physical Damage