They all mean the same thing. var. alba, var. album, fma. alba, & fma. album all refer to orchids that lack red, purple, and brown pigments. Their flowers are various mixtures of white, green, and yellow. Also, if the species usually has purple on the underside of the leaves, it will be absent too.
The reasons there are so many different names are convoluted. During the late 19th century at the height of the Victorian orchid craze, noteworthy examples of species used to be given their own variety names. Paph. insigne has dozens of these varietial names. But in the twentieth century, the only varietal names that stuck around were either distinct plants or the albino varieties. Late in the twentieth century, taxonomists decided that albino orchids should referred to as forms of the species rather than as varieties. For example, what used to be called Paph. bellatulum var. album became Paph. bellatulum fma. album.
To make things even more complicated, most slipper orchid species have formally described names for the albino forms that are different from album. You can find most of those names here:
Varietas should denote a more substantial change from the standard than forma.
Forma usually designates a group with a notable morphological deviation, e.g. glaucous leaves, white flowers and they don't need to be all closely related (e.g. separate groups that have evolved white flowers can all be f.alba / albiflorum etc.)
Varietas usually designates a group with an appearance distinct from other varieties. These are often (but not always) more than one morphological deviation or a single very substantial deviation.
I am always surprised by the range of names album forms have been given in orchids which merely serves to confuse the situation. It would be so much clearer if they had all been described as f. albiflorum (where they are actually white!).
Sometimes peoples loosely designate album all the plants that lack other colors and patterns on normal flowers .
However in reality, I believe the experts think they should be call green form or yellow form ???
Maybe some Slippertalk members can clarify this issue for us.
Fma. is the abbreviation for form (in latin) - and is used to designate minor differences from the typical form of a species. In orchids most often colour differences in flowers (e.g. P. bellatulum fma. album) or leaveage (P. concolor fma. chlorophyllum).
Var. stands for variety - and designates more markedly (morphological) differences from the typical form, but not sufficiently such for elevating the plant to the rank of an independent species.
I think a good example of this would be: Paph. hirsuitissimum var. hirsuitissimum (as the typical form will be called, when varieties have been described in the botanical litterature - though of course nobody calls the typical variety other than x 1 hirsuitissimum in the colloquial) vs. Paph. hirsuitissimum var. esquirolei.
If you read botanical litterature you will again and again encounter discussions about the taxonomic status of orchids, f.ex. is Paph. anitum a species in it's own right or is it better described as a variety of Paph. adductum, P. adductum var. anitum?
At some point in time all known plants in the section 'cochlopetalum' that we now treat as species in their own right (P. victoria-regina, P. victoria-mariae, P. liemianum, etc.) were by some authors described as varieties of Paph. chamberlainianum (as P. victoria-regina then was named).
The latter is a good example of what has jokingly, but aptly been described as the trench warfare between "lumpers" and ""spreaders" among botanists.
Then to "album": back in time it seems that botanists were inclined to designate white or other colourforms from the typical as varieties. Where as these days they use the designation form, fma.
Album - or alba if the genus gramatically is of the female gender as f.ex. Cattleya - means white in latin, and ought to be used only for all-white flowers. However the term is more often than not used as a broad term for albinistic colour forms as such.
The whole matter is a bit complicated, also due to the rules for the nomenclatura of botany, and I think the one, who best describes the kerfuffle is Dr. Braem in the article, I've attached.
Olaf Gruß takes (more or less - I haven't compared side-by-side) the same view in his monograph on 'The Genus Paphiopedilum Albino Forms'.