No, we have a republic. Fundamentally different animal.
In a democracy, the public could vote to do something that would be considered wrong such as stripping voting rights from everyone who likes country music. And with majority rule, that would pass and become law of the land.
In a republic like ours, the constitution governs what can and cannot be enacted by the majority. Since such an act would take away guaranteed minority rights, the constitution prevents the majority from doing something like that.