You are right, Handlebars and Angular together would be pretty useless.
Handlebars and Angular are completely different things.
Handlebars is a template engine. You write a fancy templatey-string, give it a JSON object, and it renders out HTML from the data. There's no data-binding, no updating, it's just a once-off render.
AngularJS is an HTML compiler and databinder. Angular will look through the HTML for angular-templating tags, interpret/compile them, and update the HTML with changes to data on a given controller scope. Angular doesn't just render an HTML string once, it compiles the HTML, binds it to a scope, and updates when data on that scope changes.
Handlebars in one picture
AngularJS databinding/templating in one picture
AngularJS's HTML compiler in one article
AngularJS's whole overview/guide, so you can know how it actually works
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