In WP `options` is the term used for variables stored in the database. They are accessed through the options API.
In WP options is the term used for variables stored in the database. Both WP core files and plugins/themes use options to store their settings. The mods of the Theme Customizer are a special kind of options.
Options are accessed through the options API. The Theme Customizer has its own API.
Options registered with autoload = yes are cached into memory on every page load, so multiple accesses to these options on a page do not mean as many actual database calls.
