Both the Galaxy Note 10 models run on the Qualcomm Snapdragon 855 chip that's powering most premium phones in 2019 — where they differ a little is in RAM.
RAM is the special kind of memory that keeps the apps you've been using running in the background. When you return to an app, the app won't need to re-open itself, and you'll be right where you left off. The more RAM, the more apps and activity the phone can store, and it can lead to a faster experience.
The Galaxy Note 10 comes with 8 GB of RAM and the Galaxy Note 10 Plus comes with 12 GB of RAM. While the Galaxy Note 10 has less RAM, 8 GB is still plenty for most people, so I wouldn't worry much about that if that's a concern.
As for storage, the Galaxy Note 10 comes with 256 GB of storage, and the Galaxy Note 10 Plus comes with either 256 GB or 512 GB of storage.