npm install: It is obvious that npm install is used to install packages using the package.json file, this command also installs the other packages on which the packages (in package.json) are dependent.
On the backside, this command uses the npm build which helps to build the packages you are installing.
npm rebuild: As the name rebuild, this command again builds the packages, used only when you upgrade the node version and must recompile all your C++ addons with the new binary.