"Democracy" isn't a standard on which our laws are (supposed to be) based, the constitution is. Hence "constitutional republic".

We use the Democratic principle of voting to choose representatives who in turn vote to enact legislation, but that legislation is (supposed to be) guided and limited by the constitution, we and our elected leaders can't arbitrarily decide laws based simply on voting for it democratically.

For instance, legally, even a supermajority in Congress and the Senate can't make a law that robs a person of life, liberty, or property (the accumulated result of living your life freely) because, even if it's voted in favor of, we are a constitutional republic, not a democratic one. The constitution can't be voted against except in some extreme case where almost all of the states get together and say "alright, this isn't working, we need to overhaul something."