An easy way to tell is to look at the back (emulsion) side. If its Kodachrome you'll be able to see a relief image as you tilt it to the light and get it just right. That is unique to Kodachrome.
Your slides may still be Kodachrome, but sheet film. It was available in 2 1/4 X 3 1/2" sheet film, among a bunch of other sheet sizes.
Finally had a chance to check the transparencies while visiting my parents at the weekend.
No relief image on the emulsion side, so not Kodachrome. No manufacturer's name or film type on the film borders so no idea what it is. I think this was 120 film as although each image is cut and individually mounted in card, the edges of some which are no longer attached to the mount aren't perfectly straight on the short side.
If only there were enough of us to be able to buy enough/spend enough to convince Kodak to make and process larger formats of Kodachrome.
But who's to say 35mm will even last for that much longer?
Kodachrome is my favorite color film...Who knows, maybe someone like Rollei or Fuji will try to get Kodachrome away from Kodak if they decide to ditch it...although I doubt it.
Fuji abandoned their Kodakchrome type products in the 80s due to low sales of all Kodachrome and Kodachrome like products. They saw the handwriting on the wall, and Kodak has been stuck with a white elephant. Beautiful, unique but hard to keep alive.
Honestly, if/when Kodak drops Kodachrome...I'm probably going to switch to digital. It is possible to get decent B&W and Velvia-like pictures, pretty easy actually. Kodachrome is really the only film that I've never seen duplicated using digital...
Okay, this gets off-topic now, but I had an add-on called "Alienskin Exposure" for Photoshop. The idea of that tool is to emulate film emulsions. Kodachrome was available there, too.
Of course I wasn't able to compare because I did not have the same pictures taken on a real Kodachrome film, but it looked very like the expected result.