The Karaim and Tzedukim are different. The Karaim reject Torah shel bal peh wherever it conflicts with what they read as pshat in posuk (which is almost always).
The Tz’dukim didn’t reject all of Torah shel bal peh, they rejected the authority of the Sanhedrin and the Perushim in expounding on Torah shel bal peh. There were large parts of Torah shel bal peh they accepted as evidenced by the arguments they have with Chazal in Menachos and other places. Tzedukim also had a very different view of schar v’onesh.