construction Type A and Type B rated buildings, rated elements, and sprinklers?

just trying to make sure i understand a code thing conceptually for testing.

anyone mind correcting how i worded this or the factual information?

Type A in Table 601 (i think) indicates a FIRE RATED building that is composed of fire rated elements as prescribed by the code for that construction type I - IV?

Type B in Table 601 indicates a NON RATED building that is composed of elements as described for that construction Type I - IV?

and then RATED ELEMENTS - like roofs or floors or exterior or interior walls (?) - can be required in either Type A or Type B?

and "sprinklering requirements" (i forget if there are any actually) or floor area increase by adding a sprinkler system (is this Table 503?) is a completely independent step from construction type or element rating.

THANKS