gstat: simple vs. ordinary kriging

Question

sorry for such a trivial question but I'm trying to find my way into the "kriging wild bush", a topic that is sometimes really confusing (at first);

do you think my interpretation of the difference between simple (sk) vs. ordinary kriging (ok) and its application in the R "gstat" package is correct?

here is my reproducible example

library(sp)
demo(meuse, ask=FALSE, echo=FALSE)
library(gstat)

# simple kriiging (sk)
# compute the mean (supposed to be known)
m <- mean(log(meuse$zinc))

# krige just the residuals
sk <- krige(log(zinc)~1, meuse, meuse.grid, vgm(.6, "Sph", 900), beta = m)

# in simple kriging (sk) the trend value (mean) is assumed to be known (constant), see beta parameter
# the kriging error only refers to the residuals

# it does not include the estimation error for the trend (mean) 
# as you would get with ordinary kriging (ok)

# ordinary kriging (ok)
ok <- krige(log(zinc)~1, meuse, meuse.grid, vgm(.6, "Sph", 900))

thanks for any feedback