Environment Variables – How to Use `env` to Print Environment in Current Shell

That depends on what you're doing.  First of all, $PWD is an environment variable and pwd is a shell builtin or an actual binary:

$ type -a pwd
pwd is a shell builtin
pwd is /bin/pwd

Now, the bash builtin will simply print the current value of $PWD unless you use the -P flag.  As explained in help pwd:

pwd: pwd [-LP]

Print the name of the current working directory.

Options:

-L
print the value of $PWD if it names the current working directory
-P
print the physical directory, without any symbolic links

By default, ‘pwd’ behaves as if ‘-L’ were specified.

The pwd binary, on the other hand, gets the current directory through the getcwd(3) system call which returns the same value as readlink -f /proc/self/cwd.  To illustrate, try moving into a directory that is a link to another one:

$ ls -l
total 4
drwxr-xr-x 2 terdon terdon 4096 Jun  4 11:22 foo
lrwxrwxrwx 1 terdon terdon    4 Jun  4 11:22 linktofoo -> foo/
$ cd linktofoo
$ echo $PWD
/home/terdon/foo/linktofoo
$ pwd
/home/terdon/foo/linktofoo
$ /bin/pwd
/home/terdon/foo/foo

So, in conclusion, on GNU systems (such as Ubuntu), pwd and echo $PWD are equivalent unless you use the -P option, but /bin/pwd is different and behaves like pwd -P.

Source https://askubuntu.com/a/476633/291937

So, what is the purpose of allowing arbitrary name in form env var=value and was it allowed by POSIX?

Quoting from POSIX: Environment Variables:

Environment variable names used by the utilities in the Shell and Utilities volume of POSIX.1-2008 consist solely of uppercase letters, digits, and the ( '_' ) from the characters defined in Portable Character Set and do not begin with a digit. Other characters may be permitted by an implementation; applications shall tolerate the presence of such names.

Note: Other applications may have difficulty dealing with environment variable names that start with a digit. For this reason, use of such names is not recommended anywhere.

So implementations of env may permit arbitrary environment variable names - and most, if not all, implementations do so, accepting every non-NUL character to the left of an '=' - and implementations of other utilities (such as the shell) may or may not permit arbitrary names.

The statement that name=value ... utility is equivalent to env var="value" utility will only be true if the implementation of env and the shell both permit name to be an environment variable.

There's an interesting Austin Group thread about this issue here: Invalid shell assignments in environment. One point mentioned is that shells generally only allow environment variables whose names can be represented as shell variables. Several participants in that thread participate in unix.stackexchange.com and can hopefully add some more info about the issue.