Saab 340 Air Taxi pilot reported an airborne conflict while on final approach. The Captain reported an RA warning as the approach to final was in progress. The Captain believes the Tower Controller may have confused aircraft in the traffic pattern.

Narrative

This was our approach to ZZZ earlier today. We were cleared for a visual approach XXR; then cleared to land once switching to Tower. We received our landing clearance on the left downwind. Downwind to base was normal; and there was traffic cleared to takeoff from XXR; as well as another airplane cleared to land (I thought I heard XXR but it may have been for XXL). Turning from base to final; just as we were rolling out on final we had a traffic alert followed almost immediately by a traffic RA to climb. At this time I spotted the traffic on our centerline and below us a few hundred feet. He appeared to be entering final from a right base at the same time we entered from the left. I was Captain and Pilot Monitoring so I called for the go-around and announced traffic in sight to my Copilot. Somewhere in here I heard Tower telling another airplane to go-around but I'm not sure if it was the plane below us or someone else. At this time I told tower we were going around; and we were directed to enter right traffic for another approach. The tower frequency was busy so I didn't initiate a conversation about what happened; we just proceeded to a right downwind and completed the next approach and landing. Tower either cleared 2 airplanes to the same Runway with no separation and we got really close; or he cleared us to parallel Runways with a crossing final approach course. Had we continued on our final approach I estimate we were about 5-10 seconds from running into the plane below us. I probably should have queried Tower about what led to this (no further explanation/apology/acknowledgement that there had been a traffic conflict was given); but my main concern was to get on the ground safely; not to risk escalating a situation over the airwaves. After landing and shutdown I didn't have a good way to speak directly to Tower and figure out what happened; thus this report.