Although these three genera of summer-flowering, deciduous shrubs are similar, they are quite easy to tell apart.
The fragrant, cup-shaped flowers of Philadelphus have four (occasionally five) petals and 20–40 stamens, while the flowers of Deutzia are usually star-shaped with five petals and 10 stamens.
Philadelphus and Deutzia are in the hydrangea family, but Weigela is a honeysuckle family member. It has funnel-shaped flowers, the five petals united into a five-lobed corolla tube (like a foxglove) with five stamens.
Closer inspection with a hand lens reveals that the leaves and flowers of Deutzia have star-shaped (stellate) hairs while both Philadelphus and Weigela have simple hairs. Deutzia has distinctive stamens with winged stalks.
With practice, these genera can be identified solely by their leaves, which are characteristically three- to five- veined in Philadelphus but not Weigela. The simple hairs of both distinguish them from stellate-haired Deutzia.

Philadelphus
petals: 4
stamens: 20–40
hairs: simple

Deutzia
petals: 5
stamens: 10
hairs: stellate

Weigela
petals: 5
stamens: 5
hairs: simple
