Online ATC uses Azure Voice to provide Text To Speech (TTS) which requires a constant connection - it’s a separate online service just like Live Weather, Live Traffic and Bing Maps Streaming in the sim.
Offline ATC uses the local Windows installation voices (specific to the localization - i.e., US English, French, etc) - it’s more stable in terms of connectivity throughout your flight but has fewer voice variety. I prefer this because I never lose ATC TTS even on long flights.