Once a program looks promising, ignore the marketing for a minute and test the itinerary. A stopover should make the trip better. It should not add a worse flight, a useless discount, or a night in a hotel far from both the airport and the city.
I start with the trip I actually need to take, then price it as a round trip, a one-way combination, and a multi-city ticket. If the stop keeps the fare close, creates real time on the ground, and does not make the transfer annoying, it is worth considering.
These terms matter because airline rules often treat them differently. A long layover may qualify for a transit hotel or tour. A stopover may require a multi-city booking or a specific stopover flow.
The word stopover gets used for different products. Before booking, separate the benefit from the destination.
Panama worked because it solved the fare and gave me enough time to see the canal. A Bogota to Rio itinerary with four nights in Panama City priced better than the direct flight.
Oman worked as a short stop, not as a full holiday. Muscat was worth seeing, but the heat changed the way I used the day. That is exactly the kind of destination where a stopover can be the right amount of time.
Turkish Touristanbul is useful for a different reason: it makes a first pass through Istanbul easy when you are tired and do not want to negotiate the city from scratch.