There are about 20,000 known lichen species. But what is meant by "species" is different from what is meant by biological species in plants, animals, or fungi, where being the same species implies that there is a common ancestral lineage. Because lichens are combinations of members of two or even three different biological kingdoms, these components must have a different ancestral lineage from each other. By convention, lichens are still called "species" anyway, and are classified according to the species of their fungus, not the species of the algae or cyanobacteria. Lichens are given the same scientific name (binomial name) as the fungus in them, which may cause some confusion. The alga bears its own scientific name, which has no relationship to the name of the lichen or fungus.
Depending on context, "lichenized fungus" may refer to the entire lichen, or to the fungus when it is in the lichen, which can be grown in culture in isolation from the algae or cyanobacteria. Some algae and cyanobacteria are found naturally living outside of the lichen. The fungal, algal, or cyanobacterial component of a lichen can be grown by itself in culture. When growing by themselves, the fungus, algae, or cyanobacteria have very different properties than those of the lichen. Lichen properties such as growth form, physiology, and biochemistry, are very different from the combination of the properties of the fungus and the algae or cyanobacteria.
The same fungus growing in combination with different algae or cyanobacteria, can produce lichens that are very different in most properties, meeting non-DNA criteria for being different "species". Historically, these different combinations were classified as different species. When the fungus is identified as being the same using modern DNA methods, these apparently different species get reclassified as the same species under the current (2014) convention for classification by fungal component. This has led to debate about this classification convention. These apparently different "species" have their own independent evolutionary history.
There is also debate as to the appropriateness of giving the same binomial name to the fungus, and to the lichen that combines that fungus with an alga or cyanobacterium (synecdoche). This is especially the case when combining the same fungus with different algae or cyanobacteria produces dramatically different lichen organisms, which would be considered different species by any measure other than the DNA of the fungal component. If the whole lichen produced by the same fungus growing in association with different algae or cyanobacteria, were to be classified as different "species", the number of "lichen species" would be greater.