Processor and Controllers always exist, no matter the data in question. They might be the same person/company/etc (as fabian pointed out) or different, but there is always a processor and a controller otherwise you are not able to apply half the articles in the law (which mention one, the other or both).
For example, in the scope of the data of your suppliers your company is likely to be the controller (you have the need for their data) and the processor (you look after that data) on your systems, etc.
In the scope of the staff that keeps your facilities clean, the controller is the company that hires that staff (lets say the cleaning company) and your company could be the “processor” in the scenario you collect their personal information to issue them badges, etc. If you dont need their data in any way (unlikely), then you are not liable.
The ICO website makes understanding gdpr pretty easy (is not that is really complicated either), in regards to the roles involved:
the point i believe Fabian is making is that his company is controller and / or processor and there is no way to select his company on the dropdown (unless he creates it as a third party as i did).
ps. GDPR is EU law and applies to all EU countries equality, there is no difference to any EU country other than the articles where the law leaves it clear to the members to adjust as wished (Rec.40; Art.6(2), etc…just search for “Member States may” on the law and you will see examples).