Teeth are together in these sounds.
The consonant sounds in "sit" and "zit" are both made by putting your teeth together and putting your tongue in the middle of your mouth, right behind your teeth, but not touching them.
If we make these sounds the same way, then what is the difference between them? The difference is not what we do with our mouths, but what we do with our voice.
When we make a /s/ sound, we do not use our voice; the sound is quiet. Put your hand on your throat and make the sound /s/. You should not feel any movement in your throat.
However, when we make a /z/ sound, we do use our voice. Put your hand on your throat and make the /z/ sound. Can you feel the vibrations?
Want to learn more? Practice the difference between the sounds "s" and "sh" with this handout.