Yep, there are differences. There are two main groups of mycorrhizae: ectomycorrhizae, generally the ones growing with trees (and also a lot of tasty forest mushrooms are in this group) and vascular-arbuscular mycorrhizae (VAM, also called arbuscular mycorrhizae/AM, or endomycorrhizae), that are called that because they make little "trees" (arbuscules) inside the root cells of vascular plants. Unless the taxonomy changed while I wasn't looking (which it tends to do a lot with fungi), AM are all in one group (Glomeromycota). AM have a special signalling dance with the root cells that allows them to actually set up shop inside special root cells, ectomycorrhizae don't do that but instead grow in between root cells and set up a sort of net they can use to catch any sugars that leak out of the plant root cells. There are also ericoid mycorrhizae, which also grow inside of the root cells, but they are only in one group of plants (Ericaceae).

Besides that, the same individual fungus can be beneficial (helps with growth) in one host, and in another either doesn't do anything or straight up steals from it (and sometimes gives the stolen resources to another host). There's a lot of trying to figure out exactly what causes a mycorrhiza to be a "cheater" or "parasite" vs a helper, sometimes it's time dependent or plant age dependent (one season it helps one member of the network, another it helps a different one), sometimes it's a preferred host thing (ok I'll help you out for now but if I find a host I like better later I'm gonna be helping them instead), there's probably some effect from whatever else the root is also infected with (plants are pretty promiscuous too and have a bunch of different fungi in different parts of their root system).

So, the short but accurate non-answer is, "It's context dependent."