Options are site specific, so you just need to use update_option()
and get_option()
.
The network-wide equivalents are update_network_option()
and get_network_option()
. Note that update_site_option()
is just a wrapper for update_network_option()
, and is an older name from when a multisite network was (confusingly) called a ‘site’. The same applies for get_site_option()
.