Simpler question about timestamp

According to the manual, all datetimes are stored in UTC/GMT values, not matter
what your time zone is.

Please correct my limited understanding below:

timestamp
    any time zone imput is ignored
    time zone demarcation in output is optional
    timestamp value is adjusted to local time zone on output
    CAN BE USED in functional indexes because no timezone change.

timestamptz
    time zone imput is required
    time zone demarcation in output is optional
    timestamp value is adjusted to local time zone on output
    CANNOT BE USED in functional indexes because no timezone change.

Anything I miss? Why use one or the other?