What are you thinking of? There is no difference between those things.
But your major point here is correct; on the fundamentals there is no reason for the English alphabet to feature a Q.
> "C" is about the same -- by itself it always sounds exactly like "k" or "s". Why not use it for the "ts" sound?
With the modern alphabet there's no reason for a C either. However, the answer to "why not use it for the 'ts' sound" is pretty obvious - that sound isn't part of the English phonemic inventory. It occurs, but that is almost always just a result of what is supposed to be a bare /t/ being followed by /s/ for grammatical reasons. (For an example of the general feeling here, note that an English word cannot start with /ts/ at all.) Why would we use any letter to represent the "ts" sound? We represent it the same way it exists in our language, as a sequence of two unrelated sounds.
> So in pinyin, zh is just like ch, but voiced.
Technically the only voiced consonants in pinyin are m / n / ng / l / r. I think a voicing contrast was present in Middle Chinese, and there's one today in Shanghainese and presumably other Wu dialects, but not in Mandarin.