Say you have a population. You take random samples repeatedly, and the distribution of all the means of those random samples is the sampling distribution. Right?
So does that mean, that if you take every single possible random sample, the distribution will be the population distribution?
On
A simple example might help: the population consists of three numbers $1,2,3$. You take all possible samples of size $2$ and calculate their means. The sample means take values $1.5$ and $2.5$ with some positive probability; hence, their distribution cannot be identical to the population distribution.
The theoretical distribution of the means of the (presumably equally sized and independent) samples will in general not be the population distribution: for example its variance will be smaller if it has one.
But as you take an unlimited number of samples, the actual means of the samples will usually be distributed closely to the theoretical distribution of the means.
It is the theoretical distribution which is called the "sampling distribution".