"nursery" ist die Baumschule.

I think "nursery" is the way to go. I'm not familiar with any other the three terms above, although I suppose they might have a different word in the UK or Australia.

To me, there is difference between a nursery (Gärtnerei) and a nursery school (Kindergarten). Try googling "nursery" and see what comes up first. Hope that helps.

I also support nursery. I've also never heard "market garden" or "gardener's house" used for Gaertnerei.

if you add "plant" as an additional descriptor there should be no misunderstandings

A plant nursery strictly speaking is a place where plants are actually grown from seed or seedlings. In the USA it is much more common to have "garden centers" where already grown plants from someplace else have been transported for further tending, but mainly for immediate sale.

agree, you would use the same differentiation in German: Garten-Center vs. Gaertnerei. A Garten-Center is simply a sales-outlet, while a Gaertnerei is also a production facility, to speak in economical terms.

I agree with 'nursery' for AE; 'market garden' is BE. 'Garden center' is also fine -- these days it may be part of a home improvement center, even a WhaleMart -- but in conversation people are still likely to say 'nursery' even if the plants aren't technically grown on site, just because 'nursery' is the more traditional term.

Another sense of 'nursery' is a room for babies, as in a hospital or a church. A nursery school is a preschool, i.e., for ages 3-4, before kindergarten. In practice, nurseries for children aren't likely to be confused with nurseries for plants.

Langenscheidt Power Dictionary Englisch

Gärtnerei (= Betrieb) market garden, AE truck garden, AE truck farm

Also agree with nursery or Garden Centre (Canada)

Never heard truck garden/truck farm and to me a market garden implies one that grows only food (as opposed to also growing decorative shrubs, flowers, trees, etc.

Never heard of truck garden/farm either, but it could be more a technical term used in the gardening industry.

Now that RES-can mentions it, the food sense of 'market garden' does sound vaguely familiar.

@ RES-can
I agree "truck garden" sounds really strange.
Wondering about the word "truck" in such a context, I found:
http://tinyurl.com/e3hvv

Truck farm is a very common term around this part of USA (NE). It refers to a farm within driving distance of a city which often supplies or sells vegetable produce in the summer at a "farmers market" or "market garden". Sometimes they are communes. Truck farming has nothing to do with ornamental plants or flowers, just vegetable and fruit produce for private home consumption.

truck garden/farm

a new one for me. Thanks!

I also agree with just "nursery", but "garden centre" is often heard in Australia.

I always thought nursery is a place where they grow plants (nurse them) and try to get new varieties of existing plants, whereas a garden center is a place where, apart from plants, you can also buy your hard landscaping, your shed, your gazebo etc