I have used them interchangeably, but I think that might be wrong. So, is this understanding of the distinction correct? Tonality is pitch affecting semantics (like the Chinese langauge), and intonation is pitch affecting syntax (like the English language, with questions), emotions (most people I guess) and the like. Is this correct?
That is not what the difference between intonation and tone is. The list of physical primitives for tone versus intonation are probably mostly the same and is more than pitch (it includes duration and phonation: intonation also involves amplitude in a way that tone doesn't). Beyond that, the difference is about distribution, function, and especially "where you do it in the grammar".
Tone is a phonological thing which is potentially lexicalizable, like nasality and rounding, and like any other phonological feature it can be exploited to make morphological and syntactic distinctions (particular syllables have their tone modified by the addition of floating tones, which may signal a particular tense or definiteness). Whatever you can mark with a segmental affix, you can mark with a tonal feature. There are cases where tone interacts with semantics, but these may be reduced to a syntactic configuration as the triggering environment. There is some controversy over what representational unit bears tone, but the most credible candidates are the mora and the syllable.
Intonation is "added on top" and exists in all languages, tonal and non-tonal. Intonation is a phonetic modification of the phonological output. The scope of intonation is much wider, being some multi-word unit of syntax (generically called "the phrase", or "the intonational phrase"). In non-tonal languages, it is generally connected to wherever the stress is (if the language has an identifiable stress location), and involves some system of manipulations of phonation, duration, pitch and amplitude. You can also modify the realization of tone with intonation, and there can be interactions between phonological stress and tone, and intonation. The properties that it reflects are more restricted. One is something about basic chunking, where it serves to facilitate breaking the speech stream up into smaller chunks, and this is more about syntactic grouping. So for example, in a structure with S V O IO Adv, V+O may be grouped together into a single intonational phrase.
What exactly you do with these chunks is, at least in some theories, a function of the repertoire of modulatory elements and their mostly pragmatic concomittants. One pattern might signal "The speaker is annoyed", another says "The speakers has doubts", or "The speaker apologizes". Intonation is not lexical (in the way that tone in Chinese or Yoruba is), and it doesn't signal case. There are some under-investigated claims about signalling negation, but generally what intonation signals is something about speaker attitude (to the extent that you can reduce a speaker's communicative intent such as requesting information or demanding something to attitude).