As already answered, yes this is a 3-way switch. The problem is that on old switches it may not be very clear which screws are brass vs. silver vs. black - after a while (50 years in a box collecting dust) they kind of all look the same...
There is a little trick you can often use to figure it out, which I am pretty sure will help you here:
Two of the wires to each switch are travelers. They will be the same colors on both switches, but those colors (out of the choices of black, white, red) will vary depending on the particular circuit, even for two different 3-way circuits in one house!
One of the 3-way switches will have a third wire, which is the incoming hot (from the panel). The other 3-way switch will have a third wire, which is the outgoing switched hot (to the light fixture). In some (not all) cases, one of the switches will have the third screw connected to the third wire in the cable that has the travelers, but at least one of the switches will not have the third screw connected to the third wire in that cable.
Once you find a 3-way switch that has two wires to one cable and the third wire to a different cable, you can start to figure it out.
- The two wires that are in the same cable are the travelers. Mark them with yellow electrical tape. (Harper's coloring scheme - it works.)
- Disconnect the third wire and cap it temporarily with a wire nut.
- Turn on power and use a non-contact voltage tester (like this one from Klein - don't use the really cheap ones that are also screwdrivers - they can be quite dangerous) to see if that wire has voltage or not. If it does, it is the incoming hot wire - mark it with black tape, unless it is already black. If it does not, then the comparable wire in the other 3-way switch should be hot and this one is switched hot, mark it with red tape, unless it is already red.
- Turn off power.
- Go to the other 3-way switch. If all 3 screws are connected to wires from one cable, you know that the two with the same colors as the other switch's travelers are the travelers and you can mark them with yellow tape. If 2 screws are connected to wires from one cable and the third screw is connected to a wire from a different cable then the two that are together are the travelers (if they don't match the colors of the other switch's travelers then STOP and upload pictures so we can figure it out, or double-check your previous work) and mark them with yellow tape.
- Mark the third wire with black tape if it is hot (because the other switch had switched hot) or red tape if it is switched hot (because the other switch had hot).
If you are replacing with new "dumb" switches then you are all set. New switches should clearly show common vs. traveler using screw colors (and in the directions). Common goes to hot (black tape) or switched hot (red tape) and travelers go to the yellow taped wires.
If you are replacing with new "smart" switches then the typical setup will have the "smartest" switch first in order to get the hot wire and neutral, but there are many different possible configurations and a lot will depend on where neutral is located, if needed. If it isn't 100% clear, add details about what you determined with the 3-way switches, what other wires are in each box (e.g., upload a picture of the other switch box) and the model # of the new switch(es). Note also that some smart switches will work with a regular 3-way switch as the second switch and some require a special "smart" remote.