OK, you've not misunderstood what I said but you've not spotted the difference with compact cameras... This may be a relatively long answer so buckle in!!
First, a definition: Focal length is the distance between the focal point in the lens (the bit where the glass elements cause the light rays to converge) and the imaging plane (the film or the sensor). It is measured in millimetres.
When you look through a camera you don't see "focal length" you see the angle of view - how wide or narrow that view is depends on the focal length. As focal length increases the field of view gets narrower and magnification increases (zooming in).
The problem is that for decades we've been used to talking about what we see through the viewfinder or on the LCD screen in terms of the focal length of the lens, rather than the field of view (measured in degrees). This is because it's easier than standardising which AoV you use (you can calculate the AoV horizontally, vertically or diagonally - see my tutorial
here for more info).
This leads to confusion. In fact, you're probably confused already. To add to this confusion, when you alter the size of the imaging device (for example APS-C sensors are smaller than 35mm film) you change the AoV. Simply, a smaller sensor means a narrower AoV. What this means is that if you look through a 50mm lens on a film (or full frame) camera the angle of view is wider than what you would see with a 50mm lens on a smaller sensor camera.
This leads to the "focal length multipliers" that people talk about. Actually the focal length is the same - 50mm is 50mm (unless the whole universe gets smaller and defies the laws of physics) but, on a smaller sensor, the angle of view is narrower and the image is magnified compared to 35mm film.
To put it another way round, to get the same AoV on an APS-C sized camera as a 50mm lens gives on a full frame camera, you need a shorter focal length.
All this confuses people so, to try to simplify things, people often convert focal lengths back to "35mm equivalents". With DSLRS this is less common now as people are more used to the 1.5x and 1.6x "crop factors".
However, with compact cameras like yours this still happens because the sensors are so much smaller than a full frame one. For example, my Nikon D90 has a sensor that is 15.6mm high and 23.7mm wide. The sensor in your TZ3 is 4.26mm high and 5.68mm wide. To put it another way, the sensor in my D90 is 15.3x bigger than that in the TZ3.
Lets re-cap... Longer focal length = narrower AoV and increased magnification (zoomed in). Smaller sensor = narrower AoV at a specific focal length (more zoomed in).
So, because compact cameras have such small sensors you have to use
really short focal lengths to get wider AoVs. What they do is replicate a particular field of view (in full frame terms) and quote the 35mm equivalent focal lengths.
Your TZ3 says 28mm - 280mm but thats in full frame equivalent terms. The real focal length is written on the lens. Around the rim of the lens it says "DC Vario-Elmar 1:3.3-4.9
4.6-46 ASPH". Thats the real detail. The actual real focal length of the lens is 4.6mm to 46mm. Because of the size of the sensor in the TZ3, 4.6mm has the same angle of view as a 28mm lens on a full frame camera.
Now the aperture thing makes sense...
f/ numbers are fractions (hence f/). It means "focal length divided by..." so f/2 means focal length divided by 2. f/2.8 means focal length divided by 2.8. They are also sometimes expressed as ratios (1:2 or 1:2.8 in this example).
Finally, we'll work one out. The actual, physical focal length of your TZ3 lens at it's widest AoV is 4.6mm. It's widest aperture at that focal length is f/3.3 (1:3.3). 4.6 divided by 3.3 = 1.39mm. So at its "28mm" setting with it's aperture wide open, the physical hole in the iris is 1.39mm across.