Why do the prerequisites to enroll in PhD programs vary between research groups in Germany?
tl;dr: You'd typically need Master's. Read on to find out why.
The "traditional" German higher education system had only one kind of a degree before PhD, the Diplom. It's typically translated as MSc and it's not wrong: basically, it was a 5 years degree. You'd typically need this degree, and having it from a university (and not a Fachhochschule, a polytechnical university) in order to start a PhD.
Then, Bologna happened.
The current scheme in Germany is: 3 years BSc + 2 years MSc. Though the initial thought was to have a US system, where most of the students exit university with a BSc, it did not took off. Most companies and universities themselves saw "just" BSc as inferior and still required a MSc degree. It got a bit better nowadays.
It is possible to get a job with a BSc, even if it would pay less.
It is also possible to start your PhD with a BSc. But it's much, much harder. In many places special "fast-track" programmes exist. Details depend on the location. Typically, they allow a future PhD candidate to study for their MSc, but in a sort-of accelerated manner, for example, the MSc thesis is then allowed to be a topic from the future PhD. Further, typically the non-MSc holders are payed less, E12 level instead of E13.
All this requires, however, further, and in some cases non-insignificant actions from the advisor. So, there might be a certain willingness to employ a BSc-holder. It might be easier, if it's a four-years BSc. The typical "fits all" requirement is, however, a MSc.
A further notice. There are two sides to doing a PhD in Germany. 1) The general advisor-student relationship. It is about research and mentoring. No money is involved in this relationship. (You might want to register as a (PhD-)student with the university, it costs not much.) 2) The employer-employee relationship. The "funded position" is not really connected to the readiness to supervise a student. (Yes, it is often coinciding, but it is not required to be so.)
My point is: you should really ask very directly, does this particular professor really want to supervise you as a prospective PhD student (even with "only" a BSc), or do they do the former and have money for your position.
- Usually, with a Master in the field of the PhD position (or a closely related field, e.g. PhD positions in physical chemistry will typically accept physicists or chemists; possibly the Master should have a grade better than x), you can be directly accepted.
- With a Bachelor (or Master from a totally different subject, or Master not from a university but a university of applied sciences, or possibly a degree from a foreign country for which there is no official declaration that it is equivalent to the Master of a German university) your application will probably have to go to a committee first who have a look at your case and decide whether and which additional courses or exams you need to take.
- If the institute you're talking of is a non-university research institute (e.g. Max Planck, Fraunhofer, Helmholtz, Leibniz): the PhD is not granted by these institutes but by the university they cooperate with. Different groups of the same institute may be cooperating with different professors from different faculties (or even different universities), and thus different rules may apply.
In most programs in Germany, the PhD is a paid position that is known as a Wissenschaftliche Mitarbeiter ("academic employee") and typically requires a master's degree as a prerequisite.
There are some exceptions to this—there are some programs where students enroll in a master's program that leads to a PhD position once the master's thesis has been completed. But such programs are relatively uncommon and should not be expected as a master's course.