I guess this is not 100% about Thai Visa,so, if the admins deem it so, feel free to delete.
I went to Mahasarakham Immigration today to submit a TM30 as I had left Thailand and returned, as required.
While I was there, I asked about the requirements for submitting a TM30 if you travel to another province.
This is the official Mahasarakham Immigration response:
If you travel within Thailand there is no requirement to submit TM30. Only if you leave the country and return.