A little bit about the history of the group first:

The Geraniaceae group is a very diverse group of plants. Whilst one type heralds from the northern hemisphere many of the sub-groups originate from south of the equator.
The two most common, the hardy north European 'Geranium' and the half Hardy 'Pelargonium' are grown extensively in the 'developed western world'
Whilst the common hardy Geranium is native to Europe the majority of what are botanically classed as 'Pelargoniums' come from South Africa. There is a great deal of confusion arising from this classification as, despite the marked difference between the two, many types of Pelargoniums are still commonly called Geraniums (see below).
When these plants first arrived in the 1600-1700’s they were considered to have a similar seeding habit to our hardy European Geraniums, hence they were originally botanically grouped with them. It was, however, understood that they had varying leaf and flower shapes and could also not withstand our hard temperate winter cold.
Their seeding habit though (the traditional birds beak) was common which suggested a genetic link.
A number of other groups of plants that were 'discovered' during this period, many also from South Africa or other parts of the southern hemisphere also had this common seeding habit.
Consequently Botanists created a new Genus to include all of the known groups under a heading named Geraniacea. They also named some of the section groups using Greek names after their bird beak characteristics.

Today the 4 most common groups are:

The Erodium (Herons Bill). Generally these are half hardy sub shrubs that in many cases grow in a similar fashion to ground covering alpine type plants. Some examples;

Erodium Pelargoniflorum

Erodium Trifolium

Erodium Manescaui

The Geranium (Cranes Bill) - this is the common north European hardy shrub that is popular to grow in the UK. Some examples are;

Geranium x 'Ann Folkard'

Geranium 'Unknown'.

The Monsonia (Monson (Lady Ann – Named after a South African Plant collector)) Generally half hardy shrub like plants that have larger base originating flower sets. Their spread from South Africa has not be so prolific so is seen less common overseas. An example is;

M. Speciosa (Photo - Courtesy of Donn Reiners, US)

And finally... The Pelargonium (Storks Bill). See this section

There has been a great deal of confusion over the years about the naming of the Geranium and Pelargonium groups. This confusion originally arose out of the original botanic classification when the Pelargonium section was lumped in with the Geranium section. Whilst the above re-classification set the rules straight over the years people have tended to ignore it. In the UK the majority of people tend to call the Angel, Scented leaf and Regal types of Pelargonium 'Pelargoniums' but still tend to call all Zonal types 'Geraniums', which of course is incorrect. In the US it's even worse as 'Geraniums' is still commonly used for all Pelargonium types.