There's a lot of nuance in exactly how you're guessing-and-checking. But... its a pretty good idea. In the case of Backtracking-search with lookahead, the "guess" is your initial label / variable assignment. When it doesn't work out, maybe you perform some kind of "learning" over the guess (why didn't it work? Can it be written into a new constraint?), and then you guess again (aka: backtracking search).
When you're out of heuristics (variable-ordering heuristics, domain ordering heuristics, etc. etc.) , your best improvement is to arbitrarily choose another variable + assignment and see if it works out. When it doesn't work, you backtrack a bit and guess again with the new information you gathered.
The question of "guess-and-check" is "how much time should I spend making a good guess" ?? If you spend a lot of time making inferences, you're doing "Strong guess and check".
If you spend almost no time making inferences, you're doing "weak guess and check".
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People who play Suduku puzzles know that "weak guess and check" solves easier puzzles faster, but "strong guess and check" solves harder puzzles faster. And worst of all, there's no way to really know if you have a hard or easy puzzle ahead of time.
So I argue that "guess and check" is a good layman's term for this whole affair. What you're calling "inference" and "unit propagation" are just the "strength of the guess"... the amount of time you spend thinking about your guess before dedicating yourself to it.
