$ b=1
$ c=$(echo $b)
$ echo $c
1

$ b=1
$ c=$(b=2; echo "$b")
$ echo "$c"
2

$ b=11; c="$(echo $b)"; echo "$c"          ### b exists in subshell.
11
$ $ b=11; c="$(b=33; echo $b)"; echo "$c"  ### $b is not replaced before
33                                         ### the subshell is executed.

$ b=11; bash -c 'echo "<$b>"'              ### b does not exist.
<>
$ b=11 bash -c 'echo "<$b>"'               ### environment b.
<11>