Thanks for adding the pics Sue, certainly very different than anything I've come across before.
The one with the cup rim and the one one with the elongated button rim both seem very unusual. The one with the cup rim almost looks similar to standard neck/rims on these bottles but looks inverted..? very confusing. The other bottle with the tall extended neck, seems to draws resemblances from other Mdina bottles in terms of the neck and button rim, but with a standard textured main body.
Have you seen anything similar to these two examples before..?