What is the difference between "mean" and "be" in regards to mentioning words?

To be specific, a student of mine wrote the sentence "便所 means stool in Japanese" and that didn't seem right to me. "便所 is stool in Japanese" seemed - again, intuitively - right to me. We had a discussion about it, and we stumbled on the topic of untranslatable words and whether or not, when attempting to explain or define the word in another language, one should use "X means Y" or "X is Y".

As an example, the word "頑張る" has many equivalents in English, depending on the context, such as "good luck" or "do your best" or "break a leg". When attempting to explain the definition of such a word in English, should one say "頑張る is to..." or "頑張る means to..."?

How philosophical do you want to get? The Japanese symbols 便所 form a label that has a meaning to Japanese readers in the same ways that the Roman letter combination stool has a meaning to English readers.^* I'll take your word that the meanings are the same. Clearly, the symbols in neither language are something you sit on; they merely label the thing you sit on, so to be technically correct you'd say

The Japanese label [word? expression?] 便所 means stool in English.

But we're used to letting context permit us laxity in differentiating between labels and the things labeled, so

便所 means stool

is likely unambiguous in a language class. Similarly

便所 is stool

in that class is unlikely to confuse students about what they're to read and what they're to sit on.

About ninety years ago, surrealist painter René Magritte warned us about the distinction in his famous painting La trahison des images (the treachery of images). (The caption reads "This is not a pipe".) But most people find they can have their pipe and smoke it too.

*I have no idea whether italicizing kanji has the same signification as italics in English, but I need some way to distinguish a symbol from what it symbolizes.)