AKISMET is the built in spam filter (see below) which comes with WordPress.com sites. Is is not included per se with WordPress.org sites. Akismet needs an API code to activate. Once you set up a WordPress.com site you can add other WordPress.org sites to your API code.
SPAM most people know as the unwanted commercial comments on their blog, its counterpart we call ham to indicate legitimate comments. On the Akismet mistakes side, missed spam is pretty self-explanatory, but a false positive is what it’s called when we incorrectly identify a legitimate comment as spam. (Which hopefully happens exceedingly rarely.)