What I'm going to write applies to 01-02 Sequoias since I see that's what you have. I have an '01 and had to do a lot of research to find the answer too.
When you press the 4wd button, the transfer case sends power to the front differential. The Sequoia has 3 open differentials: front, rear, center. The only one you can lock is the center differential, and only while in 4WD, 4L, and 1st gear. It was changed in '03 so that you could lock the center diff with a new button. To do it on an 01-02, you need to add a
center diff lock mod.
The transfer case shifter down in the center console switches between 4H and 4L. This system works really good to provide you with 2H for gas consumption, but then pressing the button puts it in 4H (basically AWD). Once you switch the transfer case to 4L, then you have the extra torque via gearing.