Why sd of a normal distribution changes by only changing its mean (R code provided)

Question

In my R code below, I'm wondering why $sd$ of N and K are larger than U?

Aren't we just manipulating the $means$ of these normal distributions, so why $sd$ changes as well?

set.seed(0)
n <- 1e5
U <- rnorm( n )         # sd = 1.00
N <- rnorm( n , U )     # sd = 1.41
M <- rnorm( n , U )     # sd = 1.41
K <- rnorm( n , N - M ) # sd = 1.73

sapply(list(U, N, M, K), sd)   # get the `sd`s

Answer 1

$N$ containts the realisations of 10000 random variables, each with a different mean. Therefore, the observed deviations from the average are higher. Same goes for $M,K$.

If you calculate sd(N-U), you should get something close to 1.