The fences are NOT used in the same manner!
On a table saw the blade is rotating vertically down towards the table. On a router table, the cutter is rotating CCW parallel to the table surface, and this makes a huge difference .
On a table saw you run the workpiece between the blade and the fence. When the blade is cutting, it's pressing the work down towards the table. The off cut can be on either side of the blade, it doesn't matter except for size or thickness.
On a router table, the workpiece is only placed on the left side of the cutter, NEVER between the right side of the cutter and the fence. In this case the cutter is spinning parallel to the table surface, not downwards like the table saw. This means any material placed between the cutter and the fence will be ejected horizontally back towards the operator..... at about 100 MPH. This rule must be followed!
With the cutter exposed to the left, and the fence controlling the depth of exposure, thee workpiece can be pushed INTO the cutter's direction of rotation safely. As with the table saw, the workpiece is fed into the blade, against it's rotation and not from behind or with the blade's rotation.
See the diagram in post number 10!