Well, .mts is a filename extension used for the BDAV MPEG-2 Transport Stream container file format. It is used for multiplexing audio, video and other streams. It is based on the MPEG-2 transport stream container. This container format is commonly used for high definition video on Blu-ray Disc and AVCHD. – from wikipedia.
Think your .mts files are AVCHD video files, that taken by high definition consumer camcorders like Panasonic, Sony or Canon…
There is some tricks to play, edit, convert the AVCHD videos, you should pay attention, not every tool can do, I don’t try if the handbrake can convert the AVCHD, as it sucks on my Mac, and I got ifunie do my help from this AVCHD essential: https://videoediting.digitalmedianet.com/articles/viewarticle.jsp?id=911450
Maybe you are not using Mac, but it would give you some ideas, and some of the apps mentioned have Windows version.
HTH 🙂
Live and let live.