There seem to exist multiple categories of theology, and people are often confounded by these categories. To explicate the meanings of some of these important fields of theological specialisation, I have adapted the following information from What Theology Is by Aidan Nichols, OP. Together with that, I have done some minor additions which I find useful:

What is faith based on?
This is fundamental theology.

Fundamental theology helps one to help other people keep the faith, by removing difficulties they may have about believing. It also helps one to convert others to the faith, by suggesting considerations relevant to the truth of Catholic Christianity.

How has it come down to us in history?
This is historical theology.

Historical theology helps one to discern the impression which Jesus Christ made upon those who first met him (the New Testament), the situation he lived in (the Old Testament) and the way his image and teaching have been preserved and presented in the Church (the history of doctrine). In these ways, historical theology enables one to put over the faith in a way that is concrete, circumstantial and historically correct.

How is its content a unity?
This is systematic theology.

Systematic theology helps one to show people how the faith hangs together, how it all makes a satisfying design which is an inspiration to live by.

How does it sound when articulated in the language and culture of particular communities?
This is contextual theology.

Contextual theology helps one to explain the faith in a culturally relevant way to particular groups of people. These groups may consist of clusters of peoples reflecting similar races, languages, nationalities, genders, etc.

What does it imply for living?
This is moral theology.

Moral theology is useful in showing people how they might be growing personally in relation to God and their neighbour.

What does it imply for the rest of what we know?
This may be termed practical theology.

Practical theology shows them the relevance of their religion to their professional work or private concerns, to their general knowledge or the social situation.