There is a genuinely interesting edge case worth knowing, because it is the closest English gets: stress-based pairs.
A number of English words change part of speech depending on which syllable is stressed — the noun and the verb forms of words like record, permit, conflict and present. Change the stress and you have arguably a different word.
That is not tone, because stress involves loudness, length and vowel quality as well as pitch, and because it is a small closed set rather than a system. Linguists sometimes call English a stress-accent language for this reason.
But it does show that the boundary is a spectrum rather than a wall. Some languages use pitch accent — a system sitting between the two — where pitch on a particular syllable distinguishes words, without a full tone on every syllable.