Don't wrap chunks of headers with extern "C" { ... }.

Don't wrap chunks of headers with extern "C" { ... }.

Instead, explictly flag individual functions with extern "C" by adding
it to the tag we're already using for exported functions, and creating a
new tag to use for non-exported functions.

Rename those tags, and the tags used for exported data, to say what they
do, rather than saying "this is an API" (we may export things we don't
want to be treated as part of the API, but that we have to export
because some programs use them).