hop 0 with tracert and pathping?

when using pathping the first line, listed as hop 0, shows the external
interface ip address of my router. Then hop 1 shows the internal interface
address of this same router. Then the rest of the list that follows is of
course outside my authority to know whether they are inside or outside
addreses.

1) what is hop 0? what is it displayed for? why is it the external interface
of my router and then hop 1 the internal address of my router?

now, jumping commands to the output of tracert, but still the same subject
matter:

2) I always imagined that the list of hops from the ouput of tracert
followed this pattern:

1) inside of your default gateway, 2) then outside interface of that same
router, 3) then inside interface of the next router in the path, 4) then
outside interface of that router, 5) then inside interface of the next
router in the path, 6) then the outside interface of that router, and so on?
is that wrong? Is it only the inside (or near side) interfaces of each
router that constitutes a 'hop' and are therefore displayed?

please enlighten me.
Thank you!