"Standard" is the old incandescent bulb/assemblies. Halogen bulbs are the very high temperature bulbs filled with a halogen gas, run at high temps, and use high purity fused silica for glass that is extremely sensitive to stuff like fingerprints on the glass. If you leave fingerprints on the bulb when you install it, the bulb lifetime will be measured in minutes.
HID, or high intensity discharge, is an arc through gas, usually xenon. It makes a very nice bright light that is best used within a 'projector' type enclosure to focus the light and keep it from spreading and blinding oncoming drivers.
And yes, halogens are standard from the factory. The old 'standard' bulbs were also known as sealed beam, and the oldest are round, then the newer ones were rectangular. The entire enclosure was sealed as a giant headlight. They are the ones that would be somewhat yellowed, and would dim with age because the filament slowly boils off and deposits on the enclosure, which is why they get dimmer. The halogen advantage is that when run correctly, the halogen gas bounces the hot metal vapor from the filament back onto the filament to keep it bright and lasting longer.
I don't know of any cars within the last 20 years or so that use sealed beams. So the current 'standard' probably would be considered halogen bulbs.
Cheers,
PH