Spore-producing organisms are called cryptogams. Ferns and fern allies are cryptogams but I say nothing about them for on the Nature Map they are included with the flowering plants. So, while the word cryptogam can be used for brevity, this means only 'spore producing organism other than ferns and fern allies'. The cryptogams are:
Mosses, liverworts and hornworts (which make up the bryophytes).
Fungi. Things such as mushrooms, puffballs, stinkhorns are spore producing structures of various fungi and spore-producing structures, in many cases ephemeral, are often referred to as fruit bodies. The permanent, feeding part of the fungus is out of sight (in wood, soil, dung, etc) and consists of a network of fine threads, called a mycelium. In essence, the mycelium is the fungal individual, just as a tree (not any of its fruits) is considered to be the individual.
Lichens, each of which is a symbiotic partnership between a fungus and an alga or a cyanobacterium. The classification is based on the fungal partner and lichens are often referred to as lichenized fungi. Those lacking symbiotic algal or cyanobacterial partners are the non-lichenized fungi. The separation of lichenized from non-lichenized fungi is artificial, with no taxonomic basis, but is nevertheless useful in everyday talk. When people use the word 'fungi' they generally mean non-lichenized fungi and that's how 'fungi' will be used in comments about Atlas of Life in the Coastal Wilderness (ALCW) Nature Map sightings. It would be mind-numbingly pedantic to say 'non-lichenized fungi.'
Algae and cyanobacteria (the latter sometimes referred to as blue-green algae).
Myxomycetes (colloquially called slime moulds, even though they are not fungi).
The Friends of the Australian National Botanic Gardens funded the production of three websites that present more information about the structures, ecology and biology of:
Fungi (non-lichenized): http://www.cpbr.gov.au/fungi/
What am I counting?
ALCW Nature Map asks for abundance information. Don't agonize over the 'correct' count for crytpogam sightings. If you see 15 wombats in a woodland you know that you are looking at 15 individuals and the count gives you useful information about the abundance of wombats, in that it gives you a minimum number for that area. When you count visible cryptogam structures you are not necessarily producing that sort of abundance information. For example. Suppose you see 15 mushrooms, all of the same species, spread over say a few square metres. Visually, it is impossible to say whether all come from one mycelium or from 15, so you do not know whether there is only one fungal individual present or 15 individual fungi. If those 15 came from the one mycelium, the count of 15 tells you as much about the abundance of that species as the count of 15 Banksia cones from one bush would tell you about the abundance of Banksia.
What is a native cryptogam?
If there is good evidence that a species has been introduced to Australia, it will be recorded as Exotic on the ALCW Nature Map. Otherwise it will be recorded as Local native (or Rare native or Very rare/Threatened if there is relevant evidence). To say that a species is native to Australia means that it occurs naturally in this country and was not introduced by humans. Since almost all vascular plants and mammals that are native to Australia are also confined to Australia, it would not be surprising if many people assumed that a cryptogam species described as native to Australia was confined to Australia. Don't make that assumption. There are cryptogams known only from Australia but there are also those that are naturally widespread, meaning that a particular species may be native to Australia as well as being native elsewhere.