Confused About Digital Signing

I downloaded a .msi file, which contains 2 executable programs for Putty (one is 32 bit and one is 64 bit). Here is where I downloaded it from.
https://www.chiark.greenend.org.uk/~sgtatham/putty/latest.html
I am trying to understand digital signing.
I have done some research and I am finding 3 different explanations about signing keys.
1- the additional file that is provided by the site, which is a .gpg file, is some kind of digital signature. But, I am a little confused as to why that's helpful. Can't (shouldn't) the digital signature be "embedded" in the .exe file?
2- I am also understanding that Windows has some built in digital signature verification (I am on Windows 8.1). Specifically, when you right click on a .exe file and select "properties," one of the tabs shows 2 digital signatures, with another column indicating Sha256, and MD5.
3- I see mention of a program, sigcheck.exe, which seems to be another way to verify a digital signature with a certificate authority.

So, again, I am a little confused as to why there are 3 methods. Are some of these just made for older windows operating systems or for some non-Windows operating systems?

 

There also seems to be something called signtool.exe
https://stackoverflow.com/questions/667017/how-to-check-if-a-file-has-a-digital-signature/22467448

 

Here's a detailed article.
https://en.wikipedia.org/wiki/Digital_signature

In a nutshell...
https://searchsecurity.techtarget.com/definition/digital-signature

 

Ok, I'm still confused.
Let's start with (1) the .gpg file. So the .gpg that they have on the site it a public key? That and the program (.exe file?) are run through some sort of algorithm?

 

A .gpg file has nothing to do with Digital Signing.

https://file.org/extension/gpg