difference between rnorm(1000, 0, 1) and running rnorm(500, 0, 1) twice

Why don't you test it yourself?

E.g.,

set.seed(42)
bob1 <- rnorm(1000,0,1)
set.seed(42)
bob2 <- rnorm(500,0,1)
bob3 <- rnorm(500,0,1)
identical(bob1, c(bob2, bob3))

I won't tell you the answer. :-)

This isn't really something that can be proved by a test.  Perhaps the 
current implementation makes those equal only because 500 is even, or 
divisible by 5, or whatever...

I think the intention is that those should be equal, but in a quick 
search I've been unable to find a documented guarantee of that.  So I 
would take a defensive stance and assume that there may be conditions 
where c(rnorm(m), rnorm(n)) is not equal to rnorm(m+n).

If someone can point out the document I missed, I'd appreciate it.

Duncan Murdoch