And what is the difference between them?
The portico is a section in front of a building's entrance, often with a floor and ceiling. Rome's Temples of Portunus Nimes's Maison Caree have good examples of the standard Roman portico, a tradition inherited from the Etruscans. They are extensions of the temple's main cella with two or three rows of columns which lead into the engaged columns that continue around the building. These creates a strong frontality in comparison with Greek porticos that could wrap around a building (e.g. the Parthenon).
A peristyle is a colonnade that surrounds a plaza, court, garden, or similar open space. The House of the Faun in Pompeii contained two large ones, as seen in its plan.