<<"From what I have seen so far, I do not see how the half fare ticket is cheaper. Do you use the public transportation in the cities and small towns a lot? How much is the fare?">>
Did you read the introduction page on "The Timetable"?
if you do, you will see this text-
<<"How to find ticket prices You can use the timetable to find the regular prices of tickets. That allows you to compare point to point tickets to pass prices. To see the price for a trip, click the 'Fare/Buy' button for your preferred travel option. Then select "no reduction", and mind the selection for single versus return journeys. Beware of the "from" prices being displayed along with the travel options. These are not the regular prices, so be sure to click the 'Fare/Buy' button. Fill out tomorrow's date when looking for prices. Prices will be the same even if your trip is much later. Prices only change once per year. For most visits to Switzerland buying a pass is cheaper than buying separate tickets for each trip. You can calculate whether that's true for your plans as well. Sometimes prices will not be displayed, or for part of the route only. That mostly happens in case of mountain trips with cable cars, funiculars, etc. In such a case you can best visit the website of the transport company for that route to find prices there. Links can be found on each of our attraction pages.">>
If you look at the screen grab I have attached, you will see fares listed of "from 20 CHF"
Those low fares are what a typical Swiss would pay (usually...sometimes there are special considerations on mountain excursion lines, etc....)...because most all Swiss have a half-fare card. To see a full fare, do as the instructions say.
In the cities-
It is too complicated for me to fully explain accurately.
I carry a Swiss resident's half fare card, so that is what I always work from.
That means when I am working the ticket machines or talking to a ticket clerk, I always get that information into the selection process.
Then, there is a multitude of options ....(different zones,"9 o'clock tickets, 24 hour tickets, regular tickets ( typically good for 2 hours in a city), "short course tickets.." which are only slightly cheaper, good for 30 minutes, regional tickets for one central city "zone" typically zone "110" to which one can add coverage for nearby zones.....)
In Zürich, if I want to go up to Uetliberg, my ticket must cover zone 110 and two other zones.
In general,for an occasional trip in the cities, I pay a few (2 or 3) CHF at the machine at the bus stop for a zone 110 ticket, making the choice shown as indicating "1/2 fare" or "children"...(same thing) and get a half fare ticket good for two hours around the center of town. The complexity arises if I plan to spend 24 hours, or, perhaps, the daylight hours, in the city and also the nearby suburbs. Usually, I get it wrong. Note that the cost of a 24 hour ticket is about 3X the cost of a 2 hour ticket.
In those more complicated situations, when I am in main stations such as Zürich or Zürich Flughafen, I go to a counter and ask, giving details of my plans. In Zürich main station, the office of the ZVV ( Zürich Verkehrs Verein) is on the lower level of the station, in the newer section of "Shopville." Some ticket machines in the main station near the railheads have a "ZVV" logo on them. Presumably, they are more oriented toward city trips.
The urban ticketing system is designed for people who live and work in the cities, or nearby. They figure all that stuff out, based on familiarity with the options. I have been using it when I come from the 'States since about 1980....and still make mistakes.
I simply waste few CHF now and then.
Hope that helps; sorry if it does not.