Tantra means a system/method. Raja means King. Rajtantra is thus a system where kings rule. In short, monarchy. The difference between monarchy and dictatorship that in the former the person gets power through lineage/family. In dictatorship, the person gets the power by himself/herself.
Lok means people. Thus, Loktantra means people’s rule. Here people have a direct say in the proceedings. In other words a democracy. It could be through elections or it could be through town/village meetings where people gather to discuss and vote.
Praja means a citizen. Not all people are citizens. Prajatantra is also a name for democracy, but a little more formal and meaning the government is of the citizens alone, not just anybody around.
Gana means a council where everyone is equal. In Vedic India, we had these councils around the country that would discuss matters of importance. Ganatantra or Ganarajya means rule by the councils. Or in short a Republic - where we have a council [Parliament] to deliberate on important issues.
A republic [Ganatantra] can be a democracy or need not be depending on how the council is chosen. China is a Republic, but not a democracy. Its council is chosen not by general elections but through a closed process within the Communist party.
In the same way, a loktantra [democracy] can be a republic or need not be. For instance, UK is a democracy but not a republic as it has a heriditary leader [Queen] as the head of the council. Switzerland is also not a republic as the people directly vote on issues rather than using Parliaments.
India became a republic in 1950, but only in 1952 it actually became a democracy - when it conducted the first general elections based on a universal suffrage.
