The pale, springy, branching stuff sold by the bag for moss walls, floristry and model scenery goes by the name reindeer moss, and like the marimo it is misnamed. It is a lichen.
Not a moss
Reindeer moss is Cladonia rangiferina and its close relatives, lichens rather than plants. Each one is a partnership between a fungus and an alga living together as a single organism, the fungus providing the structure and the alga the food it makes from light. That dual nature is why it feels dry, brittle and cartilaginous rather than soft and leafy, and why it is grey-white or pale silvery green rather than the fresh green of a true moss. Break a piece and it snaps rather than tearing. For how to tell the groups apart in general, see moss, lichen, liverwort or algae.
In the wild
Across the tundra and on northern heaths it forms vast pale carpets, springy underfoot and stretching for miles, and it is a winter mainstay for reindeer and caribou, which smell it out and dig it from beneath the snow. It grows extraordinarily slowly, often only a few millimetres a year, so those carpets represent decades of quiet growth and recover painfully slowly once grazed or stripped. That slowness matters when it is harvested commercially: a bag of it on a craft shelf may be older than the person buying it.
The preserved decorative form
Almost all the reindeer moss you can buy has been preserved. Its structure is stabilised with glycerine and it is usually dyed a vivid green, so it stays soft and pliable indefinitely without water or light. In that state it is the workhorse of preserved moss walls, wreaths, terrarium dressing and model railway scenery, valued for a fine, springy, branching texture that nothing living quite matches. It is no longer alive and needs no care beyond keeping it out of direct sun, which fades the dye, and away from damp, which can make it sticky. There is more on this use in preserved moss walls.
Can you grow it?
Not really, in any practical sense. Lichens this slow do not lend themselves to cultivation, and there is no quick way to raise a crop the way you can with a sheet of true moss. That is exactly why the supply is gathered from the wild, and why the harvest raises sustainability questions worth taking seriously. If you forage a little for a project, take sparingly and only from ground where it is genuinely abundant, remembering that what you pick took many years to grow and will take many more to return.
Why the mix-up persists
The name has stuck because the stuff behaves, at a glance, like a moss: it is low, soft-looking, forms carpets and grows in the same cool, damp, northern places. The distinction only becomes plain up close, or when you try to treat it like a moss and find it wants nothing you would give a plant. It is one of several everyday names that hang "moss" on things that are not, alongside the marimo "moss ball", which is an alga, and Spanish "moss", which is a flowering plant. Knowing what it really is changes nothing about how well it looks on a wall, but it does explain why it will never grow for you.