Guitar Cable Plugs

I thought that guitar cables have standard 1/4 inch plugs.

I’ve got a Fender Strat, and Fender Mustang amp, and two Fender cables. However, one plug on my longest cable will only plug into the amplifier and will not plug into the Strat’s input jack.

Is that normal?

1/4 inch is right - both ends. have a picture?

I have one guitar with a super tight jack. The jack has two touch points that squeeze against the cable end and I need to push in hard. It is a higher quality jack that doesn’t get scratchy since it won’t loosen up as much.

Left has two contacts, right has one in the image.