imperial garden
Refers to a garden attached to an imperial palace or residence. Often used in proper names like 新宿御苑.
Shinjuku Gyoen is a precious green space in the city center.
I like walking in the Kyoto Imperial Garden.
On my day off, I strolled through Shinjuku Gyoen.
Every spring, many people go to view cherry blossoms in the imperial garden.
公園 is an ordinary public park open to everyone, whereas 御苑 originally meant an imperial garden, even if some are now publicly accessible.
御 (honorific prefix) + 苑 (garden, park). The kanji 苑 originally referred to an enclosed garden or plantation, often associated with nobility.