The bottom navigation bar in Material Design, which I will call the bar, also known as the tab bar on iOS, is the area at the bottom of the screen that allows the user to quickly switch between sections of an app. The navigation drawer, which I will call the drawer, is typically a side sheet that displays different app sections and is triggered by tapping the hamburger menu icon.
Both the bar and the drawer can be used for navigation purposes. Many apps nowadays seem to get rid of the bar and rely purely on the drawer, especially on Android. Without careful consideration however, this can lead to usability problems.