In English, "add-on" is a generic term for any software that can be somehow added to some other software to work with it or enhance it in some way. Plug-in is a very specific type of add-on which has to conform to strict requirements for the particular software it is plugging into. Other types of add-on are NOT plug-ins. They have a different type of interface, or possibly even exist almost separate to the software they are adding to.
Hence, a plugin is an add-on, but an add-on is NOT a plug-in in probably 90% or more cases!
PS. A plugin is only a plugin if the people designing the interface decide to call it a plugin. If they use a different terminology, say a 'truc-dingle' (fictitious example), then it's a truc-dingle, not a plug-in.