They don't mean the same thing. They're not the same part of speech.
Select as an adjective has a different meaning from selected.
First of all, I've got to say that I agree with the comments you've gotten so far, in that select countries does not work well with volcanoes. In fact, I actually find it to be crude.
Second,select does mean special, but countries aren't really special for having a natural disaster occur on their soil. It's not something fortunate.
Often, in the US, you'll hear opening soon in select cities, in reference to film releases. In that context, it means specially selected cities. It also can indicate a limited, small-market film release. And it's fine to use it that way. But I would not recommend saying something like the bombings occurred in select cities. Select has a positive connotation.
As for selected, it's the past tense of the verb form of select, meaning to pick or to choose. So if you say, branches opening soon in selected cities, you mean to say that these locations were hand-picked. It doesn't have to be hand-picked; items can be selected by machines too.
If selected items are on sale, then they were picked, chosen, or designated by management. You're referring to the selection (noun) process.
If select items are on sale, then there's something special, unique, or valuable about those items. Here, select is modifying the noun items. It's not referring to the process of selection, but they may be items you'd very much like to select (verb meaning choose).
By placing 'branches' in select cities the brand did nothing to the
cities and there's no city with very unique quality in this matter.
It'll be 'selected cities'.
This can actually be either one. With opening branches in select cities, it means they were selected because there is something unique about them. Maybe they're unsaturated markets, or maybe they were chosen because the business thought they'd be more profitable in those cities. If they're opening in selected cities, that just means that the branch locations have already been selected.
Had it been the Olympic Committee's matter, we would have said, "They
organize the event in select countries."
Actually, they organize the events in the selected city. At the same time, the IOC chooses from select cities.