Geraniums vs pelargoniums

Most people  mistakenly call those "red balls of flowers" geraniums, when they are, in fact, pelargoniums!  So - what's the difference - and why do we call pelargoniums by the wrong name?

When these plants were first brought to Europe from South Africa it was thought they were the same as the European Geranium. It was later found that, though they do share many similarities, they differ in several ways. The 'new' plants were re-classified as Pelargoniums, with both the Geranium and the Pelargonium classified as genera of the Geraniaceae Family.

True Geraniums are known as Cranesbills, which refers to the shape of the seedpod.

Geraniums have: 
five petals that are the same size and shape as each other;
ten fertile stamens;
seed pods with 'curls' that act like a catapult to hurl the ripened seeds away from the parent plant;
many thin stems attached to fibrous roots;
they don't grow well in very hot, dry regions.

Pelargoniums were so named because the seedpods resemble the beak of a stork. (Pelar means stork). 

Pelargoniums have:
five petals, of which the upper two differ in shape and size from the lower three (more noticeable on the species or 'original') ;
ten stamens, but not all are fertile;
seed pods have a feathered end that enables them to float on the breeze to find a place to grow;
succulent, thick stems that hold moisture to enable them to withstand drought.

Source:  Geranium and Pelargonium Society of Western Australia

G. Magnificum

P. Mexican Sage