Should I include both package.json and bower.json?

Should I include both package.json and bower.json?

I already have a bower.json because my project is registered in it, are
there differences between the bower.json file and the package.json file
that grunt.js uses? Could this possibly work?
module.exports = function(grunt) {
grunt.initConfig({
pkg: grunt.file.readJSON('bower.json'),
...
});
...
};