All those options are actually pointing to the active theme, but the difference is the value stored in each option:
-
The options
templateandstylesheetboth store the name of the active theme folder, e.g.twentytwentyonefor theTwenty Twenty-Onetheme. But if you’re using a child theme, thenstylesheetwould be the name of the child theme folder, e.g.twentytwentyone-child. -
current_themeon the other hand (is or seems like a deprecated option which) stores the name of the active theme on the site, e.g.Twenty Twenty-One.And this option is used by
get_current_theme()(a deprecated function) and a deprecated option namedmods_<theme name>(seeget_theme_mods()).And note that I don’t have this option on my site (default install of WordPress 5.7), but if I had it, then the value would be the same as what
wp_get_theme()->get( 'Name' )returns.