The Google+ Domains API specifies a number of operations that can be done using Google Apps accounts for a domain. In PHP, these methods are
google_plus_circle_get
google_plus_people_add
google_plus_message_send
google_plus_message_read
google_plus_group_post_send
google_plus_group_post_read
google_plus_page_post_send
google_plus_page_post_read
google_plus_timeline_post_send
google_plus_timeline_post_read
google_plus_post_share_send
google_plus_post_share_read
google_plus_post_like_send
google_plus_post_like_read
Are there equivalent functions that are available if you are using a GMail account and not a Google Apps account?
Unfortunately, no. These functions are only available to Apps Domains and the accounts created for them.
The "regular" Google+ API is read-only and only works on fully public information. There are a number of open issues requesting these features, and you may wish to review the list and star those you're most interested in, giving detailed use cases where possible.