Poplars can fall into 4 groups (shown below in columns). There are many hybrids and cultivars, often difficult to distinguish. Only a few examples shown:
Lvs long & narrow (7-10x), silky on lower side; Common by streams etc. in lowland BI
Salix arbuscula . . . . Mountain willow
Damp rocky slopes and mountains in C Sc
Salix aurita . . . . Eared willow
Characteristic ears on leaf bases; esp. common in heath and scrub in N & W of Br and all Ire, uncommon in SE En
Salix caprea . . . . Goat willow agg.
Throughout lowland BI to 10 m tall; twigs not ridged (c.f. the similar S. cinerea), leaves with little point
Salix cinerea . . . . Grey willow agg. or Common sallow
To 6m tall; Has ridges under the bark of >2yo wood (c.f. the similar S. caprea); lvs hairy on lower side; the commonest Salix in lowland Br; in wet woods and marshes (sometimes split into two subspp. with subsp. oleifolia thoughout +/- BI with glossy lvs, and subsp. cinerea with lvs dull and +/- hairy on top - predominant in E Anglia)
Salix daphnoides . . . . European violet willow
Salix euxina . . . . Crack willow
Twigs brittle; scattered in wet places esp. in N
Salix gracistyla 'Melanostachys' . . . . Black pussy willow
An introduced garden plant from SE Asia
Salix herbacea . . . . Dwarf willow
A tiny plant <10 cm; Localised to high mountain tops but reasonably common in suitable situations esp. in N & W
Salix lanata . . . . Woolly willow
Densely hairy lvs with large stipules (c.f. S. lapponum); very local on mountain cliff ledges in Sc
Salix lapponum . . . . Downy willow
Lvs hairy with small or 0 stipules (c.f. S. lanata); local on cliffs protected from grazing on mountains in C Scotland
Salix myrsinites . . . . Whortle-leaved willow
Shiny green lvs; rather local in C Highlands of Sc
Salix myrsinifolia . . . . Dark-leaved willow
Lvs green on upper side, glaucous on lower, blackening when dried; local on mountains in N & C Sc
Salix phylicifolia . . . . Tea-leaved willow
N Br on base-rich soils
Salix purpurea . . . . Purple willow
Lvs hairless and mostly opposite; shrub to c. 5 m; throughout BI
Salix repens . . . . Creeping willow
A rather small shrub to about 1 m; in dune slacks and on acid heaths and moors
Salix reticulata . . . . Net-leaved willow
Very local near mountain tops in N & C Sc
Salix triandra . . . . Almond willow
Leaves finely toothed; twigs glossy, pale brown and ridged; Most common in S & E of Br and Ire
Salix viminalis . . . . Osier
Leaves densely silky hairy on lower side, not evenly finely toothed; to about 6m; Common in wet areas throughout BI exc. on mountains
Salix x fragilis . . . . Hybrid crack willow
Garden origin, widely planted and frequent in lowland Br; lvs largely hairless when mature
Salix x sepulcralis . . . . Weeping willow
Garden origin, but widely planted; weeping trees with hairless lvs even when young are S. pendulina
Also
S. alba - white willow
S. fragilis - crack willow
S. purpurea - purple willow
S. pentandra - Bay willow