For my purposes, 'classification' of flowers is far simpler and is based on the main embroidery stitch which I use to represent the flower. This varies a little, depending on the materials which I am using. Threads and wools are broadly similar, but different effects are achieved with the use of ribbons.
Most of my recent floral embroideries have been in tapestry wool against a hand-knitted background. So far, they have fallen into two 'types' -
Daisy-like - composed of straight stitches, around a French knot centre. These could be daisies, chrysanthemums, some anemones, sunflowers etc
Round-petalled - represented by blanket stitch. So far I have stitched apple blossom, and cineraria. Others will include primroses, wild roses, buttercups... ( and also 'the top of bell-shapes' such as bind weed)
Doubtless other 'categories' will follow!