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The "trap" is the bend in the pipe where the waste goes out of the toilet. It retains some water after flushing causing a seal and preventing sewer gases from entering the building.
An S-trap exits at the bottom of the toilet, and is designed to outlet directly through the floor, where a P-trap exits at the back of the toilet and is designed to outlet through a wall.
The Setout refers to the distance to the centre of the waste outlet. For an S-Trap, the setout is the measurement from the finished wall to the centre of the waste pipe in the floor (modern standards are between 140mm and 165mm). For a P-Trap, the setout is the measurement from the finished floor to the centre of the waste outlet in the wall (the standard is 185mm).
If you are replacing an existing toilet, and do not want to change the plumbing, you will need to ensure that your new toilet will fit the existing plumbing.
If you have a P Trap toilet you should not be too restricted as most P Traps have a standard set out. However, if you have an S trap toilet, you will need to make sure that you have the measurement from the wall to the centre of the trap before you purchase a replacement toilet.