Moving your configuration from one machine to another is possible, but the adapters have to match precisely since the adapter name is used a lot in the directory/file structure that describes the muxes, services and channels. If they don't match precisely, you'd need to write a routine that would rename everything (and potentially edit a file or two as well).
Have a look at /home/hts/.hts/tvheadend/dvbadapters, ../dvbmuxes, ../dvbtransports and similar.
For records of previous recordings, have a look in /home/hts/.hts/tvheadend/dvr/log. You're likely to have a mixture of files that describe both upcoming and completed recordings, although you can see the format is slightly different (e.g. the previous ones include the name of the recorded file; the upcoming ones clearly don't because there isn't a file yet).
I suppose it's possible that you can move these between systems, restart tvheadend and it'll read them in. I doubt it, though, as things are never that simple...