Those two on the right are based on Roman Current writing (that Futura is just upright version of the Italic), and two-storey a on the left has its origins in Capitalis Rustica and Uncial writing from fourth to sixth centuries, and later Carolingian Minuscule in ninth century.

The "two-story" version (example the first) is more consistent with the Carolingian miniscule rendering of the letter a, while the "single-story" version (example the last) is consistent with everyday handwriting, at least as it was practiced under the Palmer method. The middle example extrapolates Palmer penmanship with sans-serif lettering.

Is it miniscule or minuscule? And is it storey or story? :·a

Get your hands on a copy of Shapes for sounds by Timothy Donaldson. This book has some informative illustrations about the evolution of Latin letterforms.

Oh, I always thought that the single story a (and g) in Futura derived from fraktur, but then again, since the structural basis of fraktur and italic is the same, this comment might just be a matter of semantics.

Is it miniscule or minuscule? And is it storey or story? :·a

My bad: when applied to lettering, it's minuscule vs. majuscule vs. miniscule (which simply means "tiny"). Storey or story depends on whether you use British or American spelling.