What's the difference between pinery and pinetum?

Pinery

Definition:

• (n.) A pine forest; a grove of pines.
• (n.) A hothouse in which pineapples are grown.

Example Sentences:

Pinetum

Definition:

• (n.) A plantation of pine trees; esp., a collection of living pine trees made for ornamental or scientific purposes.

Example Sentences:

• (1) For services to the community in Wadhurst, East Sussex particularly to the Bedgebury National Pinetum Forest in Kent.