What is the difference between $x$ and $\{x\}$ when $x$ itself is a set? I've already asked this a part of another question, but thought it'd be easier to elaborate a bit more on my concern.
Let $x$ be a set. What is the difference between $x$ and $\{x\}$? I get that the latter is a set consisting of a single element - namely $x$, but what is the difference?
For example, we can have $x$ to be the set $\{1\}$, then $\{x\}=\{\{1\}\}$. Aren't those $2$ expressions the same?
Another problem are the brackets - when we have a set, do we always have to surround him with brackets, for instance, can we have $x$ to be the set $2$?
Thanks a lot

$$\{1\} $$ is a set whose the unique element is the integer $1$
$$\{\{1\}\} $$ is a set whose the unique element is the set $\{1\} $.
