Since I think there is a lot of overlapping of common names for these trees, I thought the definitive word from the Forest Products Laboratory of the US Forest Service might be useful, so here is the text dealing with the elms:
Ulmus spp.
this page uses English units of measure
click here to view the file in metric units
Family: Ulmaceae
click to print or download the file in .pdf format
Elm
Elm (Ulmus spp.) contains about 45 species native to Asia [11], Europe and the Mediterranean [6], South and Central America [7] and North America [7]. All species look alike microscopically. The word ulmus is the classical Latin name.
Soft Elms
Ulmus americana-American elm, American soft elm, American weeping elm, American white elm, Florida elm, gray elm, gray hard elm, rock elm, springwood, soft elm, swamp elm, water elm, white elm
Ulmus rubra-gray elm, Indian elm, it slips ooo-hoosk-ah, moose elm, red elm, red wooded elm, rock elm, slippery elm, soft elm, sweet elm
Hard Elms
Ulmus alata-cork elm, mountain elm, red elm, southern elm, wahoo, wahoo elm, water elm, whahoo, winged elm, witch elm
Ulmus crassifolia-American red elm, basket elm, cedar elm, red elm, rock elm, small leaved elm, southern rock elm, Texas elm, water elm
Ulmus serotina-Red elm, September elm
Ulmus thomasii-Canadian rock elm, cliff elm, cork elm, corkbark elm, corky elm, corky barked elm, hickory elm, northern cork elm, northern corkbark elm, rock
There is also mechanical data for the elms on the same page, here:
https://www.fpl.fs.fed.us/research/centers/woodanatomy/techsheets_display.php?geo_category_id=2&genus_commonname_criteria=c&sorting_rule=1aAs listed above, winged elm is also know here in the states as witch elm. The mechanical dats seems to place this elm first in bending strength.