Assignment of variables with space after the (=) sign?

We are not talking about two different things here.

If we had

PWD=/bin/pwd

we would assign /bin/pwd to PWD.

But

PWD= /bin/pwd

means that we call /bin/pwd with PWD set to the empty string. This assignment only affects the sub process, not the current one.

In the example PWD= /bin/pwd, the variable PWD is set to the empty string before executing the command /bin/pwd. The change only takes effect for that line.

This can be useful to make a temporary change to a variable for the purposes of running a command, without affecting the original value. Another example of this would be when using read, to set a different IFS:

IFS=, read a b c <<<"comma,separated,list"

This sets the field separator to a comma so that a, b and c are read correctly. After this line, IFS returns to the default value, so the rest of the script isn't affected.

Perhaps on some systems, the output of the command pwd is affected by the value of the variable PWD, so doing this prevents problems caused by PWD being overwritten elsewhere.

PWD= pwd

This syntax assigns the empty value to the variable PWD for the duration of the pwd command.

PWD=ick
echo "$PWD"

This assigns PWD for the remainder of the script.

PWD=ick pwd
echo "$PWD"

This assigns PWD only for the duration of the pwd command; the echo will echo the value which was in effect before and after the pwd invocation.

PWD=

This simply assigns the empty value to PWD.

Pathologically,

PWD = ick

attempts to run the command PWD with the arguments = and ick