In theory, the difference between /t͡ʃ/ with a tiebar and /tʃ/ without is that the former represents a single unit and the latter represents two units. This is sometimes important for theoretical reasons (you might want to treat /t͡ʃ/ as a unit because it lets you make some phonological generalizations) and more rarely for practical ones (Polish contrasts affricates against stop-fricative clusters: /ˈt͡ʂɨsta/ "clean", /ˈtʂɨsta/ "300").
In practice, most people don't bother to write the tie bar unless it's important (as in Polish). So I've seen both /t͡ʃ/ and /tʃ/ in different transcriptions of English, without any meaningful implication.
/ʧ/, the single character, is obsolete and no longer part of the IPA. But it would mean the same thing as /t͡ʃ/ with a tie bar: a single affricate unit rather than a stop followed by a fricative.