What are the horticultural terms for these trees and plants?

Question

Ones that reproduce through their roots with their roots, and ones that produce seeds under ground?

Also, do both of these need to be pollinated with neighboring plants to do this, or are they strictly asexual?

Answer 1

For the ones that reproduce by underground (or at the ground surface) parts these parts would be called stolons, rhizomes, tubers, or bulbs, and this is asexual reproduction.
http://en.wikipedia.org/wiki/Stolon
http://en.wikipedia.org/wiki/Rhizome
http://www.backyardnature.net/stemtype.htm
When these reproduce by having the these parts divide or break off, there's no pllenation involved.

There are different types of plants that produce seeds underground, from some orchids that never appear above ground (hypogeous, for hypo- "under" and geo - "earth" or "soil") to ones like peanuts that are pollinated above ground, but the seed develops below ground. I don't know of any special horticultural name for that. The peanut is sexual reproduction. I'm not sure if the orchid is self-fertile (pollinated within the flower) or if insects or worms are involved in cross pollinating neighboring plants.

Answer 2

Angiosperm trees and plants are broken down into monocotyledons (monocots) and dicotyledons (dicots). The former can spread by seeds or by spreading their roots underground, such as grasses and grass-like plants. The later are broadleaf plants and they do not spread by their roots underground to propagate.

Flowering plants can reproduce either by pollinating a nearby flower of the same species, or in some cases asexually depending upon the plant and circumstances. Pollen is produced in the stamens and then it is transferred to the carpel or pistil of another plant of the same species. A perfect flower has both stamens and pistils but even in these cases it may still pollinate another nearby flower and not itself. Other plants only have one or the other and must pollinate another plant of the same species.

Answer 3

Just a add on to the answer above...the peanut is consider a legume.