There is a clear difference between the two garments, the sacroiliac belt usually has smaller dimensions and is used lower, although depending on the design this may vary. It is also intended to support the sacroiliac joint, which is located just below the lumbar region.
The lumbar brace on the other hand, can be wider and its center of support is wider to occupy the entire lower back area, and although this can also occupy part of the sacroiliac joint, it does not offer as specific support as the belt specially designed for that.