Just need to get something clear. A GUI for employees managing a large scale of data, like facebook-users or whatever. Is that a form of CRM, or is CRM only business-facing?
In that case, what is that software category named?
CRM is a concept that describes Customer Relationship Management. So it can be used to describe any process that tracks an interaction with a person. Most typically between a company and a customer.
A classic example is that of a bank. You ring the bank on Monday and ask about a loan. They send you information in the post. You ring the bank on Friday. They should know that they spoke to you on Monday about loans and sent you a letter.
This may or may not use some software, although its unlikely they could just be writing everything down.
Wiki has quite a nice description:
Customer relationship management (CRM) is an approach to managing a company’s interaction with current and future customers. It often involves using technology to organize, automate, and synchronize sales, marketing, customer service, and technical support.
So that's the concept, in terms of the implementation there are a number of solutions and products which have varying architectures and are presented in different ways to both the company and customer.
For example;
Microsoft CRM, has a web page but typically this is only accessible by business users. The customers interact with the company, and the company interacts with Microsoft CRM.
However the lines can get a little blurred, for example its not unusual for companies to build self-service portals which integrate into Microsoft CRM. In this way customers are directly interacting with Microsoft CRM.
In terms of your points:
A GUI for employees managing a large scale of data, like facebook-users or whatever. Is that a form of CRM
I would say yes. However it could also cross into sentiment analysis, and data mining.
is CRM only business-facing?
As described above, CRM is a concept. Its implementation is often business facing only, but not always.