They solve different problems, and plenty of homes need both. Here's how to tell which one you're looking at.
You probably want a softener if: there's white scale on fixtures and shower doors, glassware comes out spotted, soap and shampoo won't lather, laundry feels stiff, or your water heater has failed earlier than it should have. That's hardness — calcium and magnesium. A softener uses ion exchange to reduce those minerals.
You probably want filtration if: the water tastes or smells off, there's a chlorine smell, you're seeing orange-brown staining (iron) or black specks (manganese), there's visible sediment, or a test came back showing something specific.
Both, in many cases. Hardness and iron together is common. So is hardness on a well that also needs a sediment pre-filter. When both are needed they go in a particular order, and getting that order wrong shortens the life of the equipment.
Whole house or one tap? Point-of-entry treats everything, including the shower and the water heater. Point-of-use treats one faucet, usually the kitchen sink, and costs less to buy and maintain. Which makes sense depends on what you're treating and why.
Start with a test, not a catalogue. Your water, not a regional average. On a private well nobody tests it but you. On municipal water the utility publishes a report, but that describes water at the plant, not at your tap after it's been through your pipes.
On certifications. We only say a system is designed to reduce something when the media is certified for it — NSF/ANSI 42, 53, 58 or 401, depending. Ask us and we'll show you the certification for whatever we quote.
If your test comes back clean, we'll tell you that.