When you say "First" and "Second", are you referring to the true release dates in the UK, or the confusing, out-of-sequence release dates in the US?
Not counting their appearance on Tony Sheridan's album, their first UK release was Please, Please, Me, released March 22, 1963. Their second was With the Beatles, November 22, 1963. Their first release in the US was Introducing ... The Beatles, released on Vee Jay records on January 10, 1964 followed by Meet the Beatles, 10 days later, on Capitol records. The Beatles Second Album was released in the US on April 10, 1964. That makes it the third Beatles album released in the US, and the sixth or seventh album release overall, including the UK and Canada. The Beatles Second Album was a rehash of their second UK album, With the Beatles. Capitol did some serious tweaking of some of the UK recordings, like lots of extra reverb, to simulate "sheer rock power" that wasn't originally there in the studio.
I confess that I had to look up all those details. I knew that the release dates of their albums in the US was confusing, but I hadn't memorized the details. I had to research those details above.