Tvheadend

Did you ever find out what the difference is?

An ageing post, but I'll answer anyway...

Stream Profiles what gets used when handing the stream over to another client to play (e.g. VLC, Kodi), with or without transcoding.

Digital Video Recorder Profiles what gets used when recording a file directly from tvheadend.

My suspicion is that - for whatever reason - the OP's default format simply changed and can be changed back. Both .ts and .mkv are simply containers, and will hold the audio/video as broadcast - i.e. an MPEG-2 video stream with stereo MP2 or AC3 audio, or H.264 with 5.1 AC3. It's just like putting it into a differently-shaped box, but it doesn't change the contents. Arguably, .ts is more suitable as it's a passthrough container and doesn't try to be clever with the streams, but .mkv is fine if it works for you.

Converting to MP4 suggests a recode to H.264, so you're changing the AV stream at that point as well as the encoder. Again, the source container makes no difference at that point... you're better off choosing one based on your workflow: if you edit out commercials, and your commercial-editing software prefers .ts, then use that; if you create EDLs, and your commercial skipping software prefers .mkv, then use that.