Isn't it frustrating to go to the store and look at that wall full of spatulas, trowels and glue spreaders. Why are there so many? Which one do you need for your job?
First the difference between flexible and rigid spatulas. If you have ever tried to apply thick window putty with a rigid spatula, you probably just had the putty pull away from itself more than flow into the joint -- like in the first photo. The second photo shows using a flexible putty knife with thick putty. Move with a very low angle and a lot of pressure to create a curve to the blade. This will flow that thick putty into place, with the excess flowing out to the sides. No putty is moved along with the knife, so it does not pull away from itself.
When you work with soft materials, like drywall compound, now you want to scrape off excess as much as apply material. Very little pressure is required pushing towards the surface. So use a rigid spatula and run it close to 45 degrees from the surface. That will keep a supply of compound in front of the spatula to fill in as you go, removing as much as it is putting on and not really pushing much off to the sides, where it only makes a mess.
If you attempt to apply adhesive with a smooth trowel you will get some areas with all the adhesive scraped off, and others with too much adhesive. That is why glue or adhesive spreaders always have teeth. The teeth pattern and size is specific to each adhesive and applies a carefully and easily controlled quantity to the surface.
First read the can of your adhesive. It will specify the size and shape of the teeth you should have on your spreader. On the TV show I showed what happens with different techniques. You should try it yourself.
First spread some adhesive with the trowel straight up. Then do some more with the trowel at 45 degrees to the surface, then again almost flat. In every case push hard enough so that the teeth drag on the surface, leaving no adhesive where the teeth touch. You will see that the first pass applied far more adhesive than the last. If you were to push a transparent tile into each of the adhesives, as in the fourth photo above, you would see: the first one would trap air pockets in the middle and excess glue would come out all the sides. The last one would leave gaps between the adhesive lines, giving less than a full bed of adhesive. The one spread with the trowel held at 45 degrees to the surface will allow the air to flow out between adhesive lines and the lines will just barely close up when the tile is seated, with no gaps and no overflow. That is why each adhesive and each application requires the proper toothed trowel, and the proper technique of application.
When working with concrete -- do not ever use a steel trowel. For some reason it tends to draw too much water to the surface, making for very weak concrete. Adding too much water to concrete and too much smoothing off are the primary DIY errors in working with concrete. Always use a wooden trowel or a magnesium float, and just barely get the concrete flat, never over smooth the top surface. You want it flat, slightly rough with no standing water. That makes for a long lasting concrete surface.