Q. the key of solomon vs the greater key vs the lesser key

i am struggling to find the difference between the following books:
the key of solomon
the greater key of solomon
the lesser key of solomon

in the wikipedia article key of solomon it says:

L. W. de Laurence in 1914 published "The Greater Key of Solomon", directly based on Mathers' edition, to which he made alterations in an attempt to advertise his mail-order business (for example by inserting instructions like "after burning one-half teaspoonful of Temple Incense" along with ordering information for the incense).

i interpret this as "Mathers' edition" is "the key of solomon" since that is what the article is about. but there is a book called "the greater key of solomon" by mathers so i'm confused. here are the different books on amazon:
the key of solomon the king by s. l. macgregor mathers
the greater key of solomon by s. l. macgregor mathers
the lesser key of solomon by aleister crowley and s. l. macgregor mathers (i wonder what the difference between the crowley and mathers-only version is?)

anyone care to enlighten me?

update/answer: when you look inside the greater key of solomon the first page has the title "the key of solomon", NOT "the greater key of solomon", so it seems as if my hunch was correct. but the odd thing is that underneath in latin it reads "clavicula salomonis" which translates to "the small/lesser key of solomon". it should read "clavis salomonis" (the key of solomon). in other words "the key of solomon" is the same as "the greater key of solomon".

check the latin to english translation yourself