is a two pin button the same as the arduino four pin button?

I tried to use a 4 pin button as I didn't have any 2 pin buttons but it didn't work

this link is to Instructables where I tried to do a project with the Arduino 4 pin button
(it came with the starter kit)

link: https://www.instructables.com/id/StopIt-LED-Game-powered-by-arduino/

Yes, they are the same, but those 4 pin buttons are internally connected like this:

So if you use the wrong 2 pins, i.e. 2 pins that are always connected, like A&D or B&C, then it does not work. You should use 2 pins that are normally not connected: A or D on one side, B or C on the other side.

Easier: use diagonal pins. A&C or B&D. Then it does not matter which way round it is installed.

Or you can nip off two diagonal legs and it becomes a two pin button:

A useful point to make, I think, is that components have datasheets (or should have) - all questions
ought to have an answer in the datasheet. Its not impossible for some random manufacturer to come
out with a 4-pin button switch with a different pin-out (unlikely, but not impossible) - so always check
datasheets if you want to avoid mistakes...