Ultralight aircraft pilot reported a NMAC in the traffic pattern.

Narrative

On descent into ZZZ I was handed off from flight following with ZZZ approach to ZZZ tower. On initial contact with ZZZ tower about 5nm away; they asked to confirm I was type Skylane. I corrected 'negative; type Pipistrel Sinus; PAPA INDIA SIERRA INDIA.' Tower acknowledged the transmission. Tower instructed me to enter left downwind for XX. I acknowledged. When I reached midfield on downwind; tower cleared me to land XX number 2 behind a Twin Star on final. As I began my base leg turn; tower instructed a Diamond single engine on a straight in approach that they were cleared to land number 2 behind a 'light sport on final.' The Diamond pilot responded acknowledging the transmission and that they were looking for traffic.' As I finished my base leg; tower asked the Diamond Single if the had me in sight. They confirmed 'negative still looking for traffic.' At this moment I called up to correct that I was on base; not final. Tower then instructed the Diamond single to make a 360 for spacing. At this moment I got visual of the Diamond single as they began their 360 and as I was turning final. They were maybe 500ft behind me; and 50-100ft above me. Both of us landed without incident. It seemed as if tower misjudged my approach speed not realizing my aircraft performance (thinking I was a SKYLANE for some reason; which has much different performance from the self-launch glider I was flying); and gave incorrect guidance to the other aircraft on my actual position; leading to a near miss because the other aircraft was looking in the wrong place because Tower had given them incorrect information on my location. I was left wondering whether I had misunderstood where I was supposed to be in the landing sequence; but was not reprimanded or given a number to call; so I think I was in the right spot. Tower did not seem to have the bandwidth to discuss over the phone since the same controller was working both TOWER and GROUND at this airport; so I did not seek any 'post-mortem' clarification after landing and parking.