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In programming, memoization is an optimization technique that makes applications more efficient and hence faster. It does this by storing computation results in cache, and retrieving that same information from the cache the next time it's needed instead of computing it again.
The term "memoization" was coined by Donald Michie in 1968 and is derived from the Latin word "memorandum" ("to be remembered"), usually truncated as "memo" in American English, and thus carries the meaning of "turning [the results of] a function into something to be remembered".
Memoization is the top-down approach to solving a problem with dynamic programming. It's called memoization because we will create a memo, or a “note to self”, for the values returned from solving each problem.
Caching Data is a process that stores multiple copies of data or files in a temporary storage location—or cache—so they can be accessed faster.
Memoization is a specific form of caching that involves caching the return value of a function based on its parameters.
Caching is a more general term; for example, HTTP caching is caching but not memoization.
Wikipedia says:
Although related to caching, memoization refers to a specific case of this optimization, distinguishing it from forms of caching such as buffering or page replacement.
As I have seen them used, "memoization" is "caching the result of a deterministic function" that can be reproduced at any time given the same function and inputs.
"Caching" includes basically any output-buffering strategy, whether or not the source value is reproducible at a given time. In fact, caching is also used to refer to input buffering strategies, such as the write-cache on a disk or memory. So it is a much more general term.
I think term caching is usually used when you store results of IO operations, or basically any data that is coming to you from the outside (files, network, db queries). Term memoization usually applies to storing results of your own computations, for example in the context of dynamic programming.
Memoization is a special form of caching the result of a deterministic function. This means that caching the result outside the function is not memoization because the function would have to mutate the cache when computing a new result (not already in the cache) so it would not be a (pure) function anymore. Memoization generally implies passing the cache as an additional argument (in an helper function). Memoization will optimize functions that need to compute values several times for a single access. Caching will optimize functions that are called several times with the same parameters. In other words, Memoization will optimize the first access whether caching will only optimize recurrent accesses.
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