What is the distance of a full lap in professional horse racing or are some tracks different?

Tracks are definitely different in size and shape.

Melbourne's Flemington racecourse "is shaped not unlike a pear, and boasts a six-furlong (1200 m) straight known as 'the Straight Six.' The track has a circumference of 2312 metres and a final straight of 450 metres for race distances over 1200 metres."

https://en.wikipedia.org/wiki/Flemington_Racecourse

"Caulfield race track, home of the the Caulfield Cup and is operated by the Victorian Amateur Turf Club, Melbourne Victoria. The track has a circumference of 2,080 metres and the home straight is 367 metres long. The course has sweeping long corners and there is a rise along the back of the course leading to the 1,400m start. The sharp corners and the short straight make it difficult for horses to come from the back and win."

https://www.progroupracing.com.au/australian-racecourses/caulfield-racecourse

The starting position of each race is adjusted so that the appropriate distance has been covered when the horses reach the finishing line, whether that is the first time around the track or after a later circuit.