What is the difference between the universe and the galaxy?

The word universe basically means everything that is, including galaxies and whatever lies between the galaxies.

A galaxy is a large collection (millions or billions) of stars held together by gravity. We live in a galaxy called the Milky Way galaxy.

Before it was realised that there were other galaxies, the word universe was used of our galaxy.

When it was discovered that there were other galaxies, the term "island universe" was used for galaxies for a while, but it has dropped out of usage nowadays. In some ways it is still an appropriate term because it would be very difficult, impractical or pretty much downright impossible to travel to another galaxy due to the enormous distances involved.

One galaxy you can see - at least partially - with the naked eye is Andromeda - the largest galaxy in the Local Group. The Milky Way is the second largest and the Triangulum Galaxy is the third largest. There are about 50 galaxies in the Local Group, mostly smaller satellite galaxies.

The Local Group of galaxies is part of the Virgo Supercluster of galaxies, containing at least 100 groups of galaxies.

The Virgo Supercluster may itself be part of the Laniakea Supercluster of about 100,000 galaxies.

It is estimated that there are about 100 billion galaxies in the observable universe.