If algorithm really is meant only for puzzles "related to algorithmics", as its tag description states, then I expect that most questions actually tagged algorithm had better be tagged strategy instead. I see several algorithm questions related to Rubik's cube and none asking whether some task is $NP$-complete or the like (which would in any case belong better at https://cs.stackexchange.com/, I think).
Strictly speaking, algorithm and strategy are different concepts, and not every strategy can be formulated as an algorithm.
For example, in the Prisoners Problem with infinitely many prisoners and accepting the axiom of choice, the prisoners have a winning strategy, but no winning algorithm.
As it often happens, the mathematical distinction isn't mirrored in everyday language (I'd expect the average SE user to think of a strategy as a type of video game, and an algorithm as a piece of code to make random numbers or sorted arrays) and that's the reason why the tags seem to be used interchangeably.
If you look further in the algorithm tag wiki, it defines an algorithm as
a process or set of rules to be followed in calculations or other problem-solving operations (especially by a computer).
Really, an algorithm is just a strategy for solving a problem which can be described by a discrete list of precise rules. The concept of "algorithmics" is not constrained to theoretical CS concepts like complexity, computability, languages, etc. It is about anything which can be solved by an algorithm, which does encompass Rubik's cubes, water measuring puzzles, lights out, etc. For these problems, the tags algorithm and strategy are equally valid.
Furthermore, algorithm puzzles don't always require finding an algorithm, but simply involve using "algorithmic reasoning." This usually boils down to finding some sort of invariant or non increasing quantity. In the chameleon puzzle, the invariant is the mod 3 difference between the numbers of each pair of colors. Also, this includes information theoretic concepts that show up in liar and weighing puzzles, like, "if there are $n$ possibilities, then it takes $\log_2 n$ binary tests to find the correct one," which comes from the pigeonhole principle.
In summary, I think the scope of the algorithm tag is
Any puzzle whose solution is an algorithm
Any puzzle which uses algorithmic reasoning, like invariants, the pigeonhole principle, the extreme value principle (any finite set has a largest element), modular arithmetic, etc.
While the scope of the strategy tag is
- Any puzzle whose solution is a strategy (this further includes "escape from this situation" puzzles)
Neither tag is a subset of the other.