Can anyone explain to me the difference between the OTP (one-time pad) and Vernam Cipher? I heard they are very similar, although there are subtle differences between the two.
Confusion arises because many people use the terms Vernam cipher and one-time pad interchangeably--but they are not the same thing.
When young Gilbert Vernam, an AT&amp;T research engineer, got his patent in 1919 (for a &quot;Secret Signaling System&quot;), Vernam cipher meant a fast encryption method using an additive stream cipher that was machine-based and used Baudet with modulo 2 addition.
XOR was born.
According to this unclassified NSA historical account (p.2):

Gilbert S.Vernam, working on new developments in telegraphy, came up
with a novel (and relatively simple) scheme for encrypting TTY. He
mixed  two  Baudot-coded  punched  paper  tapes (hole  being  a  “+,”
no  hole  a  “-”): one  tape  contained  the plaintext message and the
other the “key.” These tapes were added  “modulo  2”  (“exclusive
or”)  in  a  mechanical  tape reader producing an output cipher signal.

This was a huge improvement over the tedious codebooks and the German ADFGVX cipher, which was susceptible to cryptanalysis. Interestingly, in 1918, the U.S. Army was uninterested in Vernam's work.
But there were several problems no one understood at the time:
1.  The key had not been generated in a truly random manner
2.  The key was on a looped tape
3.  The key was reused

Not a one-time pad.
Enter Joseph Oswald Mauborgne--artist, cryptographer, and U.S. Army General-- the first person to send a radio signal from an aircraft to the ground.  He had the realization that if the key had been generated in a random manner, then the ciphertext from Vernam's machine would be unbreakable.
Frank Miller, an American cryptographer, had already invented the one-time pad in 1882, but the glory seems to have landed on Gilbert Vernam instead of the two people who had actually figured it out.  This reminds one of how Blaise de Vigenère had a cipher named after him that Giovan Battista Bellaso had invented much earlier.
Vernam cipher and the OTP are not the same thing.  Moreover, when we say OTP that can refer to a physical object, usually one that is easy to hide and destroy.
These days, we mostly think of the OTP as a model for encryption systems.