Science and Philosophy are two types of ______
Solution 1:
The term I use for this is lens in the sense of
something that facilitates and influences perception, comprehension, or evaluation ("Lens." Merriam-Webster.com. Definition 5.)
Some examples of usage:
Some scientists . . . have been outspoken about the satisfaction they find in viewing the world through both a scientific lens and one of personal faith. (Science and religion: Reconcilable differences)
Reading Through a Disciplinary Lens
Connie Juel, Heather Hebard, Julie Park Haubner and Meredith Moran
Understanding how to think like a scientist, writer, or historian can provide students with new insights as they tackle a text.
(Article in March 2010 Educational Leadership)
When you study biopsychology, you examine memory, perception, cognition and behavioral disorders through the lens of physiology, neural biochemistry, biophysics and anatomy. ("What is Biological Psychology?" Learn.org.)
You can also usefully extend the metaphor by thinking about different kinds of literal lenses. For example, bifocals use different lenses to assist with near- versus far-vision; lenses can be used to isolate certain details, or combined to create various effects; and so forth.
So for your title question,
Science and Philosophy are two types of lenses.
You could also combine this with @alwayslearning's suggestion, for disciplinary lenses, or choose your own adjective: conceptual lenses, theoretical lenses, etc.
Solution 2:
The first word I could think of is disciplines (though already mentioned in comments). Further, where your "thinking spheres" overlap, it can be termed as interdisciplinary.
M-W:
discipline noun
3 : a field of study
Filtered through scores of later interpreters, it percolated across a broad segment of academic culture and influenced disciplines as diverse as literary criticism and legal theory.
interdisciplinary adjective
: involving two or more academic, scientific, or artistic areas of knowledge : involving two or more disciplines
Solution 3:
Lacking additional information on what you are seeking, I would call science, philosophy, religion, and spirituality subjects.
From The Free Dictionary:
subject: a course or area of study
Solution 4:
You have sort of answered it in one way in the statement of your question itself: They are types of "approaches". Calling them "Knowledge spheres" is creating another terminology that needs to be explained. One would then ask, what is a "knowledge sphere", what is "Knowledge", and what is "sphere", why call it "sphere", etc. Of course, a question still remains, which is: "approaches" to what? The answer to this new question would depend on the the writer's perspective and the context in which the statement is written.
Solution 5:
You've already accepted an answer, but it is not one word, and you've indicated that neither individual word is exactly what you're looking for. Given that, I thought I'd try two additional possibilities: perspective and worldview.
From The Free Dictionary:
perspective:
a mental view or outlook; an understanding of how aspects of a subject relate to each other and to the whole
a way of regarding situations, facts, etc, and judging their relative importance
one's mental view of facts, ideas, etc., and their interrelationships
It's fair to say that different people have different perspectives, be they scientific, philosophical, religious, or spiritual. For example, one might say, "From a scientific perspective, ..." or "From a religious perspective ..." Perspective has some of the same connotations as lens.
From Wikipedia:
A comprehensive world view or worldview is the fundamental cognitive orientation of an individual or society encompassing the entirety of the individual or society's knowledge and point of view. A world view can include natural philosophy; fundamental, existential, and normative postulates; or themes, values, emotions, and ethic.
It's fair to say that different people have different worldviews, be they scientific, philosophical, religious, or spiritual. So, one might have a scientific worldview, a religious worldview, ...
Of these two possibilities, perhaps perspective comes closest to the word you're seeking.