Pelargonium gets its name from the resemblance of the shape of the fruit to the beak of a stork, which is pelargos in Greek. The species name laevigatum, comes from the Latin laevigo or levigo, meaning ‘smooth’, which possibly refers to the smooth and fairly succulent leaves.

The species was first described by Swedish botanist Carl Linnaeus the Younger, under Geranium laevigatum, from a specimen brought to him by Carl Thunberg collected in the Cape between 1772 and 1775. In 1860 the section Glaucophyllum was described by Harvey and he placed the then P. laevigatum in the section. Schoncken suggested that 3 subspecies should be distinguished and this resulted in Pelargonium oxyphyllum and P. diversifolium been reclassified as subspecies of P. laevigatum and are now known as P. laevigatum subsp. oxyphyllum and P. laevigatum subsp. diversifolium respectively (Van Wyk & Van der Walt 1995). Despite more work being done on the section by Van der Walt et al (1990) it was decided to keep the species in the section.

The subspecies diversifolium and oxyphyllum can be distinguished from the subspecies laevigatum as follows:
The leaves of subsp. laevigatum are always trifoliolate (a compound leaf with 3 leaflets) and the leaflets are variously incised (have deep cuts into the margins), they are hairless to sparsely covered in stiff, coarse hairs; and the flowers are borne in pseudo-umbels of 1 to 5 flowers.
Subspecies diversifolium (hairy fine-leaf pelargonium) has both unifoliolate (leaves with one leaflet) and trifoliolate leaves, with leaflets that are not incised, and the leaves are hirsute to densely hirsute (covered in stiff, coarse hairs); it bears 1 or 2 flowers per pseudo-umbel; and it occurs in the Western Cape between Gydouw near Ceres and the Robinson Pass between Oudtshoorn and Mossel Bay, on lower mountain slopes and hills.
Subspecies oxyphyllum (Cedarberg fine-leaf pelargonium) has trifoliolate leaves with leaflets that are not incised, and the leaves are hairless; the flowers are usually borne singly, and it only occurs in the Cedarberg Mountains between Wupperthal and Citrusdal, in deep sandy sandstone soil in flat areas.