There are no “universal” terms. You used hash as an example, that’s already less universal than calling it a dictionary - it’s a hash map/table, and I’ve only ever heard this term from Perl developers.
"table" is shorter than "dictionary" and also describes the structure better. A dictionary is mostly a book, or a list of keys (/usr/share/dict). prolog also used the term "table" or "tabling" for its caching of backtrackings, what we would call "memoize" or memoization via a hash table.
It's a practical certainty that the vast majority do not, and its design (up to Perl 5, at least) smacks of total Lisp ignorance.
"Map" is used in mathematics as a kind of synonym for "function", especially from some arbitrary set to another one. If you assign the domain < 1, 2, 3, 4 > to the range < 3, 2, 4, 1 >, that's a map. We can draw it as two bubbles containing labeled dots, and draw arrows between the bubbles.
This sense of "map" is widely used in computing. For instance "keyboard scan codes get mapped to characters" or "a coordinate in the abstract canvas get mapped to the viewport, which is mapped to the screen" or "the temperature sensor is mapped to GPIO-s 13 to 17."
The "map" in Lisp's mapcar is exactly this sense. The map is the function that is being applied: mapcar is using the verb sense: take the car of every cell through the function: i.e. map each domain value to the range. This is called "projection" or "mapping"; "map" is just the verb describing what happens to each individual element.
https://groups.google.com/forum/?hl=en#!msg/rec.arts.startre...
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But at least he knew the terminology, and got the concepts right. In opposition to php and python which failed miserably.