electoralism

Ya there's a few other quirks that come along with it I think. Governments can be dissolved and elections called much easier, for instance

For one, a third party can gain a foothold much more easily. In the UK, for example, small parties to the left of Labour can win and hold seats in Parliament.

It's about how much power the head of state has. If they directly run the government and make policy, presidential (or Prussian Constitutional, in the case of a monarchy). If they don't and the power is defacto devolved to a parliamentary cabinet appointed by the representatives, parliamentary. If you're the French and De Gaulle fucked up your government to maintain power, semi-presidential.

The advantage of parliamentary systems is they fail quickly and cleanly. If the governing representatives lose the ability to vote in a budget, they're not in power anymore (either a new coalition forms organically, or elections are called), while a US system can fuck around for decades with an inability to pass policy. The downside is the difficulty in making and maintaining stable majorities, see Belgium.