Plans

Appropriate Technology
Steal buildings and plans from a planet. "Appropriate" is just bureaucrat speak for stealing something.
Planetary Command Center
The planetary command center (PCC) houses the central government for your empire. This is your "flag in the ground" that lets everyone know you've staked your claim to a planet. It provides some basic resources and and storage for those resources both of which increase with the level of this building. The planetary command center also provides some critical reports on your planetary activities such as total resource production and total resource storage for the planet it's constructed on. It's one of the most versatile buildings in the game, but it's also very expensive to upgrade.
Plans
A plan is a build or upgrade of a building that you get for free. There are six ways to get plans in the game: contests, spies, the Archaeology Ministry, Excavator, trading, missions, and the tutorial.