A park is a landscaped area serving for relaxation and to increase the prestige of a town/city.
A public garden is a site featuring trees, bushes, lawns, flowerbeds and footpaths primarily serving the purposes of relaxation and to make a city more beautiful.
Such areas are generally classified as urban open space and thus as settlement area.
[Source: AdV (2008): GeoInfoDok, ATKIS-Objektartenkatalog Basis-DLM, Version 6.0]