My camera, aimed at a motionless object, is mounted on a tripod. Do I get a different image by changing exposure time and the diaphragm in such a way that the total amount of light coming in stays the same?
It depends on what is on your picture. Short vs long exposure obviously gives different look if shooting moving objects. Even tree in modest wind can be a moving object if exposure is long enough. Or a cloud. And aperture determines the depth of field, so if you have some objects outside of the focusing plane, they will look more or less blurry depending on the aperture number.
The aperture also somewhat impacts image quality. Wide open lens may show some optical aberrations and very narrow aperture (like f/16 or f/22) may introduce some blur due to light diffraction.
As you mentioned that the total amount of light (eg exposure) would stay the same, the main difference you will see is in the depth of field. A smaller aperture (bigger f number) will give you a deeper depth of field - that is more things are (or more of the main subject is) in focus. For subjects with a light source you may also start to see a star-burst effect with a smaller aperture. Other than that if you are compensating the aperture changes with an opposite shutter speed change you will keep the same exposure.
The 3 main things you have at your disposal to alter the exposure are shutter speed, iso and aperture. They have the following effects (in a nutshell):
- Shutter speed - mostly effects motion, can have effect on saturation (long exposures)
- iso - mostly effects graininess of final image
- aperture - as mentioned, depth of field control, also some other effects like star burst from bright sources which is more pronounced on long exposures.
You can alter one of those to change the exposure or multiples of them to keep the exposure the same but achieve a different result in your image.
That's why the "program shift" is the first non-automated thing you should learn. Let the camera suggest an exposure, but then use the knob to switch between equivalent exposures, to fit your artistic aims.
Knowing how these affect the picture is the first thing to learn. Examples: change the aperture to ensure enough depth of field or throw the background out of focus; adjust speed to freeze the action or show motion (a waterfall will show very different images fast and slow).
So, learn what the effects are, in principle. Then use "program shift" to apply those ideas. Take multiple shots with different (equivilent exposure) settings, not just to see which you like best but to further get a feel for what they do.
You mentioned motionless in particular. So, if the shutter speed doesn't matter to the resulting image, the affects of the aperture still will.
Shooting products for sale or food we've cooked, I have that situation. So I use a low ISO setting and furthermore use a cable release cord, so I can use whatever shutter speed balances the equasion, even if it's very slow.
For the aperture, I'll use the sharpest setting for that equipment. Then also take additional shots with smaller apertures to ensure the depth of field is enough or as a failsafe in case the focus was a bit off.
Consider a slice of cake with the bulk of the cake behind (another example). Trying each different aperture and letting the speed be whatever it takes, you can see the difference in how sharp is the cake in back when the focus is on the slice in front. Or, if the depth becomes too shallow (large aperture) the slice might not all be in focus, as it's a few inches front-to-back.
Try it. A non-moving subject and tripod is ideal for seeing that yourself. Take a shot with each different aperture setting you can, and look at them.