The Great Andromeda Nebula and Andromeda refer to the same astronomical object, which is the Andromeda Galaxy (also known as Messier 31 or M31). However, the terminology used to describe it has evolved over time.
In the past, before the true nature of the Andromeda Galaxy was fully understood, it was commonly referred to as the Great Andromeda Nebula. Nebulae are clouds of gas and dust in space, and when early astronomers observed Andromeda, they initially categorized it as a nebula.
It was only in the early 20th century, thanks to the work of astronomers such as Edwin Hubble, that it was confirmed that the Great Andromeda Nebula was, in fact, a separate galaxy outside of our Milky Way. This realization led to a shift in terminology, and the object became known as the Andromeda Galaxy to reflect its true nature as a distinct galaxy like our own.
So, to summarize, the Great Andromeda Nebula and Andromeda both refer to the same object, the Andromeda Galaxy, but the former term was used historically when its true identity as a galaxy was not yet known.