Creepa if you have a classic style terrarium (ferns, begonias, etc) that moss would work great planted and allowed to spread. Another easy way to tell if it's sphagnum is it doesn't have those spore/sperm pouches on the little flower stalks like the clumps in your pic. I've seemingly lost my bryophytology book and I can't remember what they're called one of you other geeks is gonna have to hit me over the head with a defenition here!
If you want some live sphagnum then the best, surest way is to buy some plain old dried LFS and grind it up really good doesn't have to be dust but what you wanna do is bust up those heads in the LFS that house the spores so they can be freed to germinate. Lay about 1" deep layer of the ground LFS in a "Jiffy greenhouse" (the black tray with the clear lid sold everyhere for starting seeds) and let it sit in decent light (not direct sunlight or under metal halides) and keep misting it every week or so and in a few months you'll have a patch of Live sphagnum to crop from. Replace harvested spots with more ground LFS and moisten, easy breezy! Get several trays going and only harvest from each one every month or whatever so there's never a shortage. When I would harvest it I would chop the handfull into very small bits and "inoculate" the tops of my pots and the min-spahgnum bits would start all new cultures.
Moss is fun stuff, those clumps of dirt and cap/forest/etc moss you have can be put into a blender (dirt and all) with a can of beer and ground up into a paste, and "painted" with a clean (cheap) paintbrush onto driftwood to grow moss if it stays moist and illuminated. Have fun!
BTW any green slime/algae spots that show up pluck them out when you see them that'll ruin your LFS culture.
You'll often get ferns and all kinds of neat stuff growing out of your LFS when it's "germinated" in this way - I even got a sundew once! I suppose it depends on where the sphagnum is from. The old "crappy" brand Mosser Lee that harvests in Wisconsin never had live sphagnum growing out of their LFS instead everything else under the sun grew out of it. Mostly sedge grass and weeds. Get the Blonde New Zealand Spahgnum and it will grow if conditions are met - with the occasional fern or liverwort making an appearance. They start as a furry "foot" (which I often mistake for fungus until studied with a 30x lense) then some weird fronds will start coming up, then more and more mature fronds. I try to wait til they get about 2-3" before I move them to their own pot of LFS.
....it's 5 am and I'm rambling again, I just hit edit to tell ya about the algae thing...