Checks can be a bit tricky to define. According to the official definition : "Pokémon A checks Pokémon B if, when Pokémon A is given a free switch into Pokémon B, Pokémon A can win every time, even under the worst case scenario, without factoring in hax." But obviously, some checks are better than others. I'd call a hard check something which can't switch into every move a Pokemon can fire at it, but switches into most of them, and, more importantly, can easily switch into the most likely or most commonly used move move. For instance, Latios is a hard check to Keldeo, since it switches into every move bar Icy Wind with relative ease, and can OHKO from there. It's also a hard check to Landorus-I, since it takes nothing from earth Power, Focus Blast or Psychic and OHKOs back. It's not a counter, since it can't switch into Knock Off, but it does have a relatively easy time switching in on Landorus-I, so it's a very good check.
A soft or shaky check would be something that cannot switch into most moves the opposing Pokemon carries or switch into a move it is likely to use, and/or needs prior damage to beat it. For instance, Life Orb Mamoswine can't switch into Latios's Draco Meteor, and needs chip damage on it to guarantee to KO it with Ice Shard, it therefore qualifies as a soft check. This also applies to Pokemon that can beat other Pokemon under specific conditions (like Ferrothorn vs Keldeo locked into Scald, or Thunderbolt Latios vs an Azumarill which just used Belly Drum). I don't really think there's much of difference between soft counters and shaky ones, but I'd guess that a shaky check needs a bit of luck on its side to win . For example, LO Gengar checks Unscarfed Tyranitar just as long as Focus Blast hits.
Again, it's pretty hard to define what is and isn't a check, especially when you delve into the territory of revenge killing, but basically, a check should be able to switch in on one move from the opposing Pokemon and either beat it or heavily cripple it (for instance, Thunder Wave Slowbro can't do too much to Charizard-X in terms of damage, but it can paralyze it for the rest of the team to deal with it). Also, the more likely you are to be switching in on a move that doesn't damage or cripple you a lot, the better a check you are in general.. I hope this helps.
