There seem to be two questions here.
The name 'communicative language teaching'
Names of things have a history, and they do not always accurately describe the thing named. Communicative language teaching, according to the Wikipedia page, has a greater focus on communication as a goal and a method of teaching than some other methods.
How is it different
The main question is: Different from what? There are many methods and the lines between them are unlikely to be bright and clear.
Quotes from Wikipedia:
Language learners in environments utilizing CLT techniques, learn and practice the target language through the interaction with one another and the instructor, the study of "authentic texts" (those written in the target language for purposes other than language learning), and through the use of the language both in class and outside of class.
I have taken many language courses which used a textbook, rather than natural texts. Use of the language outside the class, or even within the class, was not always emphasized.
Learners converse about personal experiences with partners, and instructors teach topics outside of the realm of traditional grammar, in order to promote language skills in all types of situations. This method also claims to encourage learners to incorporate their personal experiences into their language learning environment, and to focus on the learning experience in addition to the learning of the target language.
Many language learning methods do not focus on personal experiences or sharing them. The introspective dimension suggested above has been absent in most language learning of mine.
According to CLT, the goal of language education is the ability to communicate in the target language. This is in contrast to previous views in which grammatical competence was commonly given top priority. CLT also focuses on the teacher being a facilitator, rather than an instructor. Furthermore, the approach is a non-methodical system that does not use a textbook series to teach the target language, but rather works on developing sound oral/verbal skills prior to reading and writing.
Language might also be learned as an intellectual exercise, as a help to understanding other languages more deeply, to be able to read (but not necessarily write, speak or listen), in order to appreciate a culture, etc.
Many language teaching methods do have an explicit teacher and do use textbooks. Reading and writing are emphasized in many methods.