SonarLint lives only in the IDE (IntelliJ, Eclipse and Visual Studio). Its purpose is to give instantaneous feedback as you type your code. For this, it concentrates on what code you are adding or updating.
SonarQube is a central server that processes full analyses (triggered by the various SonarQube Scanners). Its purpose is to give a 360° vision of the quality of your code base. For this, it analyzes all the source lines of your project on a regular basis.
Both SonarLint and SonarQube rely on the same static source code analyzers – most of them being written using SonarSource technology.