One of my bryology students told me that their friend could not believe that they were taking a course on mosses. Their friend's comment was that there is only one type of moss, right? The small green kind.
This question boggles my mind. Is there only one kind of bird? No. One kind of tree? No. One kind of moss? No. You have to get pretty specific in your definition of any living plant or animal before the answer to that type of question is yes. For example, is there only one kind of ostrich? Yes. Only one sugar maple tree? Yes. You get the idea.
So my point is there are many different types/species of mosses in the world. Just take a look at some patches of moss when you are out and about. I bet that when you get close to the mosses and really peer at them you will notice that the first patch does not look exactly the same as the the second patch.
The question that I more often get but have a hard time answering is, "How many species of mosses are there worldwide?". This presents a problem, because it depends on who you ask and whether they are a splitter or a lumper. (Basically - A splitter is a scientist who tends to find differences between organisms and then groups them in a way that creates more species. A lumper is a scientist who would look at the same organisms focus on the the similarities and then group them in a way that creates fewer or one species.) Those are not technical biology terms and these are my own informal definitions, but if you were to use either of them with a biologist who thinks about species they will most likely know what you mean.
In the end this makes for a difficult question "How many species of mosses are there worldwide?" I have looked through a number of bryology and botany books on my shelves and here is the range of answers to this question. (The quotations are arranged in chronological order.)
Bryophyta by Parihar (1961) p.150 "... about 660 genera and 14,500 species."
The Structure and Life of Bryophytes by Watson (1971) p.16 "Some 14,000 species of moss are known and the great majority are sufficiently alike in structure to create a real difficulty for the taxonomist."
Biology of Plants by Raven, Evert and Eichhorn (1999) p.412 "...at least 9500 species of mosses, with new forms being discovered constantly, especially in the tropics."
A Checklist of the Mosses by Crosby, Magill, Allen, and He (1999) p.1 "This Checklist recognizes 12,754 species. Although new species of mosses continue to be described, the number being recognized appears to be declining, because of increased synonomy."
Introduction to Bryology by Schofield (2001) p.10 "... contains approximately 10,000 species in nearly 700 genera."
Bryophyte Biology edited by Goffinet and Shaw (2009) Ch. 2 p.56 "With approximately 13,000 species, the Bryophyta compose the second most diverse phylum of land plants."
Introduction to Bryophytes by Vanderpoorten and Goffinet (2009) p.70 "Approximately 12,000 species are currently recognized,..."
From this survey we end up with an answer that ranges from 9500-14500 species of mosses. Scientists are usually comfortable with a high level of uncertainty so they may find that range a sufficient answer. Remember it's not as though there is a right answer and by giving a range scientists just don't know. The number of species is constantly changing as new ones are discovered and others may go extinct. It also depends on which expert you consult (splitter or lumper). So the answer to this question is in a constant state of fluctuation.
I find that giving a single number is more satisfying if I do not want to go in the the whole explanation that I have given here. Usually I say that there are approximately 12,500 species of mosses and I quote A Checklist of the Mosses as my source. This count is going on ten years old at this point, but I think that it is the most accurate count that we currently have. It also looks like the two books from 2009 are following this count as well with their values that are a little above and below those of the checklist.
So, "How many species of mosses are there worldwide?" you may ask.
To that I would answer that there are approximately 12,500 (Crosby et al 1999).