Both. Sort of. Alabama (and every other US state, as well as the US as a whole) is a republic, which is a form of democracy in which representatives are elected to debate and vote on issues. (In a true, or direct, democracy, every issue is voted on by the population as a whole. This is obviously a bit unwieldy for large populations; some towns in the US are actually run by direct democracy, but it's not all that common.)
Historically, "Democratic Republic" usually meant "socialist". "People's Democratic Republic" (or "Democratic People's Republic" meant "really, REALLY socialist".
The United States government is a democratic republic.
Kinshasa is the capital of the Democratic Republic of Congo, in Africa.
Alabama Republic ended in 1861.
Alabama Republic was created in 1861.
republic
The Roman Republic was neither authoritarian nor democratic. It was oligarchic.
Democratic Republic of the Congo
The leader of the democratic republic is Toma.
Finnish Democratic Republic ended in 1940.
National Democratic Party of Alabama was created in 1968.
Alabama National Democratic Party was created in 1968.