No, your first cousin once removed is your first cousin once removed. Your second cousin is your second cousin. Two different things!
To understand how it works, take a look at this imaginary family:
Generation 1: Robert-------->(siblings)<----------Sall…
Generation 2: Mary-------->(1st cousins)<-------Lisa
Generation 2: Molly------->(2nd cousins)<------Lindsay
Generation 4: Callie------->(3rd cousins)<------Ashley
Robert and Sally are siblings.
Their children, Mary and Lisa, are 1st cousins.
Mary and Lisa’s children, Molly and Lindsay, are 2nd cousins.
Molly and Lindsay’s kids, Callie and Ashley, are 3rd cousins.
The “removed” comes in when you’re talking about cousins who are in a different generation from each other. Take Mary and Lindsay, for example. They’re one generation apart, so they would be 1st cousins once removed. Mary and Ashley are 2 generations apart, so they’d be 1st cousins twice removed. Molly and Ashley are second cousins once removed, because they’re 2nd cousin, one generation apart.
Make sense?