You get EMF from a change in flux. Doesn't matter how, and there is no way better than any other.
You have to be really particular with your vocabulary to start, so first, notice the difference between "field" and "flux".
Diagrams usually help. Try this:
http://www.sparweb.ca/2_Gen_Ax/AXIAL_FLUX_HowItWorks_V4.pdfThe field is there, always, around a permanent magnet, no matter what you do. The field is represented by the lines drawn in loops from N to S.
Those lines always want to make a complete circuit. In fact by definition, they are never "broken".
At any given spot, you can measure the intensity of the field with a gaussmeter. The result is measured in "gauss" or "Teslas" (which is the same, just 10,000x more)
The flux is something else. Flux is the amount of the field that passes through an area.
The area you use can be almost any size, but it does have to be flat. Circular, rectangular, triangular, star-shaped, cloud-shaped, it can be any flat shape that is convenient.
You don't need a magnet to have flux through your area, either. The earth's own magnetic field is passing through it to begin with, so every loop of wire encloses a bit of flux.
When you do hold a magnet up to the area, then you can talk about a sensible amount of flux. It's the average intensity of the field, pointing through the area, times the area.
Those field lines that don't pass through the area don't count. If a line goes in and also comes out of the area then it doesn't count either. This is called "flux leakage".
To be efficient you want as many of those lines from the magnet to go through the area of your coil. It also doesn't matter if the lines are centered or off to one side, if there are the same number of field lines passing through anyway. The lines have to go through the area at right angles to be fully counted, too. Field lines going through the area at a 45 degree angle only create 70.7% of the flux.
The units of flux are in Tesla X square meter (or square inches but then you have to use a conversion). That's also called a "Weber".
You still don't have an electromotive force, until you change the flux. The way to change the flux can be ANY way you like. Change the field, change the area, it doesn't matter.
Move the magnet relative to the area, mov the area relative to the magnet, reverse the magnet, reverse the area, adjust the magnet's field (electromagnet), adjust the size of the area, it all causes a change in flux.
The flux also changes over a certain period of time. Do it fast, and you get a greater EMF. So EMF has units of "Tesla X square meter / second". The combination of those units is also called a "Volt".
Changing the orientation of the magnetic pole through the area of the coil is just one convenient way of rapidly changing the flux. Causing the change by moving the magnet is electrically the same as causing the change in flux by moving the coil.