The word localization is a new and, in my opinion, an annoying addition to geomatics. The question used to be: What is the difference between positioning and location? Two possible answers to which were:
- they're the same thing
- the difference depends on a specific context
One context was AVL (automatic vehicle location). In the late '80s, Hassan Karimi coined the term PLANS for "positioning, location and navigation systems". While it didn't catch on, it does relate closely to your question. In that context, positioning was determining coordinates (what the P in GPS stands for), location was finding that place on the map (or the nearest point on a road network to that position), and navigation was finding routes to other places on the network.
If that is correct, then you have your 1 and 2 in reverse order.
Now to the (IMO, ugly) word localization. I often see it used in the context of trilateration where position must be determined from multiple distance measurements to control points. In that case it is synonymous with positioning. However, I believe the more common use, especially in IT, of localization is "the process of adapting internationalized software for a specific region or language by adding locale-specific components and translating text." wikipedia