In the past they were, but, present day, they do not precisely
refer to the same footwear. The plimsoll originated in England in
the 1800's, and is therefore an English term in origin; the term
"sneaker" is a US term applied to the same footwear in
the 1900's. The shoe both terms referred to had a basic canvas upper
and flat rubber sole: ideal for "sneaking" up upon someone.
The meaning of the terms diverged after the 1950's. While the meaning
of the term "plimsoll" has remained the same up until
the present day, referring only to above shoe, the term "sneaker"
has not. In the US the term sneaker refers to any kind of casual
sports shoe - including the plimsoll. In the UK the term "trainer"
has a closer meaning to the term "sneaker".