Looks like English people who know about plants call both a daisy, too ...
http://www.rhs.org.uk/Databases/HortDatabase....HORTICULTURAL DATABASE SEARCH RESULTS
Bellis perennis
(Bellis perennis L.)
an accepted name in the RHS Horticultural Database
DAISY;BAIRNWORT;BANWOOD;BANWORT;BENNER GOWAN;BONE FLOWER;BONEWORT;BRUISEWORT;COMMON GOWAN;DOUBLE DAISY;EWE GOWAN;GOOSE FLOWER;GOWLAN;HERB MARGARET;LOCKIN GOWAN;LUCKIN GOWAN;
MARGUERITE;MAY GOWAN;NOON FLOWER;PASQUARETTE
HORTICULTURAL DATABASE SEARCH RESULTS
Leucanthemum vulgare
(Leucanthemum vulgare Lam.)
an accepted name in the RHS Horticultural Database
OX-EYE DAISY;MARGUERITE;BIG
DAISY;BULL
DAISY;DOG
DAISY;DUN
DAISY;ESPIBAWN;FIELD
DAISY;HERB MARGARET;HORSE
DAISY;HORSE GOWAN;LARGE WHITE GOWAN;LOVE-ME;LOVE-ME-NOT;MATHES;MAUDLINWORT;MIDSUMMER
DAISY;MOON
DAISY;MOON FLOWER;MOON PENNY;POOR-LAND
DAISY;PRETTY MAIDS;SHERIFF PINK;WHITE CAP;WHITE
DAISY;WHITE GOLDES;WHITE MAN'S WEED;WHITE OX-EYE;WHITE WEED