Air taxi Captain reported during short final approach another aircraft landed on the same runway; opposite direction. Air taxi flight crew performed a go-around and returned to land.

Narrative

During our arrival into ZZZ we were talking to ZZZ center who let us know there was a cirrus jet arriving to the field before us landing runway XX which matched what our plan was as well. The winds were 240° at 10 kts with clear skies. At 25 miles out we had the field in sight and canceled our IFR clearance and went to XXX.X for traffic advisories. I was the pilot flying and the first officer was making all appropriate radio calls for our plan to fly over mid field and enter a left downwind. The cirrus jet landed and there was a Cessna following them in on a left base and a Comanche had just taken off all on runway XX. We had lots of separation between all traffic but we continued making the radio calls for left downwind; base and final. At the 500ft the first Officer called out stable" and I called out "landing." At 100ft I reduced the power to idle and just above the runway started to flair. The first Officer called out Go Around twice very quickly and on his second call I added go around power and executed the go around without touching down. Briefly looking up I saw a jet on the opposite end of the runway coming towards us with their spoilers up making me believe they had just landed. During the go around we flew over the jet that had landed by maybe 100-200ft. We continued the go around up to pattern altitude of 2100ft. We never received any alerts on TCAS or any other indication that there was another jet landing or in the vicinity of the airport. We entered a left downwind and that's when we heard aircraft X make a radio call saying "mic check; sorry I had swapped frequencies and didn't realize it." After flying the pattern and landing on runway XX we saw Aircraft XY holding short of the runway waiting to depart. When we were doing our shutdown checklist the pilot of Aircraft XY came over the radio and apologized for not making calls and again said he thought they were having radio issues. After shutdown I advised the passenger that we had to do a go around due to another aircraft on the runway and he was not upset or bothered that we did a go around."