Q:

Difference between quote and expression in R

gettypes = function(x) {paramx = substitute(x); print(typeof(paramx)); print(class(paramx)); print(mode(paramx))}
gettypes(expression(sin(x+y)))
# [1] "language"
# [1] "call"
# [1] "call"
gettypes(quote(sin(x+y)))
# [1] "language"
# [1] "call"
# [1] "call"
expression(sin(x+y)) == quote(sin(x+y))

Error in expression(sin(x + y)) == quote(sin(x + y)) :
        comparison is not allowed for expressions

identical(expression(sin(x+y)), quote(sin(x+y)))
# [1] FALSE
x = 1
y = 2
eval(expression(sin(x+y)))
# [1] 0.14112
eval(quote(sin(x+y)))
# [1] 0.14112

They look pretty much the same.

A:

expression returns its arguments as a vector of unevaluated expressions.
quote returns its argument as an unevaluated expression.

Try this:
(e1 <- quote(sin(x+y)))
# sin(x + y)
(e2 <- expression(sin(x+y)))
# expression(sin(x + y))
str(e1)
# language sin(x + y)
str(e2)
# expression(sin(x + y))
str(e2[[1]])
# language sin(x + y)
all.equal(e1, e2)
# [1] "Modes of target, current: call, expression" "target, current do not match when deparsed"
all.equal(e1, e2[[1]])
# [1] TRUE

Another example:
e2 = expression(sin(x+y), x+y)
e2
# expression(sin(x + y), x + y)
e2[1]
# expression(sin(x + y))
e2[2]
# expression(x + y)

