So it's sort of like "[masculine] garden of animals". When do you use גינה and when do you use גן?
Usually a smaller garden (like the one some people have in their house or a small vegetable garden) is referred to as "גינה". Larger gardens, like a zoo, a playground, heaven or a kindergarten are referred to as "גן".
I was just thinking of the word garden that I learned somewhere else long ago, and it came right away here ! Silly, but nice & refreshing..
It is interesting that they keep only two kinds of animals, it could be for tax optimization.