Is Blog Admin or Site Admin

is_site_admin is deprecated, WP3 uses is_super_admin – wp-includes/ms-deprecated.php

is_user_member_of_blog will return true or false – wp-includes/ms-functions.php

Is there something that returns true if a user is the original blog admin?

current_user_can

https://codex.www.ads-software.com/Roles_and_Capabilities

Example:

if(current_user_can('manage_options') {
// do stuff only blog Administrators can do
} else {
// do something everyone can do
}

Not sure what you mean by “original blog admin” but I use this to return the username and avatar of the admin email user:

$id = $current_blog->blog_id;
$user_id_from_email = get_user_id_from_string( get_blog_option($id, 'admin_email'));
$details = get_userdata($user_id_from_email);
echo get_avatar( $details->user_email, 32 ).' ';
echo $details->user_firstname.' ' . $details->user_lastname.'<br />';

So putting those to notions together, I could change the output based on whether the user logged in the “owner” of the blog

$id = $current_blog->blog_id;
$user_id_from_email = get_user_id_from_string( get_blog_option($id, 'admin_email'));

if($current_user->id == $user_id_from_email) {
echo get_avatar( $details->user_email, 32 ).' ';
echo $details->user_firstname.' ' . $details->user_lastname.'<br />';
} else {
echo get_avatar( 'default', 32);
}

Thanks
I think that might be what I am looking for.

What I mean by “original blog admin” is the user that originally owns/manages the blog.

Say like I create a user “joe1” with a blog.
I add other users, “john1” and “john2”.
“joe1” would be considered the original blog admin.

So I am thinking that with what you said, anyone who has the “manage_options” permission is the blog administrator. But what other permission is unique about the original blog admin that we could add in conjunction to “manage_options”?

https://codex.www.ads-software.com/Roles_and_Capabilities

“manage_options” is a cap all blog admins share:
There are no permissions associated with the admin_email user, unless you code them yourself.

activate_plugins
create_users
delete_others_pages
delete_others_posts
delete_pages
delete_plugins
delete_posts
delete_private_pages
delete_private_posts
delete_published_pages
delete_published_posts
delete_users
edit_dashboard
edit_files
edit_others_pages
edit_others_posts
edit_pages
edit_plugins
edit_posts
edit_private_pages
edit_private_posts
edit_published_pages
edit_published_posts
edit_themes
edit_theme_options
edit_users
import
install_plugins
install_themes
manage_categories
manage_links
manage_options
moderate_comments
publish_pages
publish_posts
read
read_private_pages
read_private_posts
switch_themes
unfiltered_html
unfiltered_upload
update_plugins
update_themes
upload_files

Oh, a couple of those caps get bumped up to the Super Admin Role in a multisite install: edit_themes, edit_plugins, install_plugins, install_themes, etc.