Question about "AT TIME ZONE"

The following is taken from section 9.9.3 of the help docs
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Examples (supposing that the local time zone is PST8PDT):

SELECT TIMESTAMP '2001-02-16 20:38:40' AT TIME ZONE 'MST';
Result: 2001-02-16 19:38:40-08

SELECT TIMESTAMP WITH TIME ZONE '2001-02-16 20:38:40-05' AT TIME ZONE 'MST';
Result: 2001-02-16 18:38:40
The first example takes a time stamp without time zone and interprets
it as MST time (UTC-7), which is then converted to PST (UTC-8) for
display. The second example takes a time stamp specified in EST
(UTC-5) and converts it to local time in MST (UTC-7).
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In the first example it says it is converted to PST "for display". In
the second example it is not converted to PST for display. Does this
mean that if a timestamp *with* a timezone is specified, and it also
includes "AT TIME ZONE", that it is not converted to PST "for display"
at the end?

I just want to make sure that these two examples perform completely
different tasks. Essentially the first item:
SELECT TIMESTAMP '2001-02-16 20:38:40' AT TIME ZONE 'MST';
And this:
SELECT TIMESTAMP WITH TIME ZONE '2001-02-16 20:38:40-07' AT TIME ZONE 'PST';
are the exact same thing.

Kind of confusing.

Regards,
Collin