Any discrepancy you may see occurs because the tools are using slightly different expert bases.
The Who Should I Start (WSIS) tool compares players solely using expert rankings that have been submitted for that position. If you're comparing players from different positions, then the tool solely uses expert rankings that have been submitted for flex rankings. The Sit/Start Assistant only uses rankings from experts who have also submitted QB, WR, RB, TE, flex, K and DEF rankings. There are some experts that only submit QB, WR, RB, and TE rankings, so the Sit/Start Assistant excludes these experts from its expert pool.
This results in the expert base for the Sit/Start Assistant being a little smaller than that of the WSIS tool by several experts. If you choose your experts for both tools so that the same expert rankings are being used for each tool, then you'll notice that both tools will choose the same player to start.