There are several good reasons for an International Driving Permit. It is, as graup said, only a license for foreign countries so they are able to see what your original license permit, it is itself invalid (!) in your home country. You need to have a license of your home country to get an International Driving Permit and you get the IDP automatically if you request it, so your question of procedural difference is obsolete.
First, no policeman is able to verify that that thing you are giving him is a valid driving license, especially if it is in Cyrillic or some other cryptic language. Do you know how a Chinese or Ethiopian driving license looks? I do not, and I assume that most people don't know either. While the "Vienna Convention" requests that you should need your original driving license, I never take it with me (no one cares and as you need a valid license to get the IDP, it is stupid).
Second, your assumption "I always assumed that if I have a driver's license from one country, it only depends on agreements whether I can drive with that license in another country." is wrong. There is a known problem in the EU that people drinking or speeding and losing their driving license hope to get away if they renew it in another EU country. No, it does not work this way.
Another problem is that there are different regulations in different countries. Heavy trucks or buses may be only moved in the EU with special licenses and/or medical tests for reaction time and eyesight. You may be forbidden to drive a motorcycle. The International Driving Permits are using the least common categories to solve this problem.
While I do not know if this happens, there is the possibility that some countries have such a bad standard or no license at all (small isle countries ?) that people from this country simply may not get an international license and may not drive.
The procedure to get a normal driving license for cars in Germany is as follows: You visit a "Fahrschule" (a driving school, a private institution with a certified teacher), you need to visit at the very least 28h theoretical classes, 5 overland journeys, 4 autobahn journeys and 3 night journeys. If you think you are ready, you will be tested both theoretically and practically (practically with an independent scrutinizer which gives you often some ugly traps). After the test your scrutinizer gives you your license.
With that you go to your local public authority and get your IDP without any hassle.