Looking at the Corpus of Contemporary American English, I get the following data. (the chart shows the result of the search, which include phrases using bothThe sentences use either the singular andor the plural of the words.):
Looking at the sentences included in the CoCA, it doesn't seem prerequisite is used with different meanings.
Does one seem like a prerequisite for the others?
Since primacy in undersea warfare is a prerequisite for other naval operations, priority must be given to expanding the navy's edge […].
According to Humboldt (Aksan, 1998), language is a prerequisite to the materialization of thought.
The prerequisites of these procedures are the reader's actual and fictional encyclopedias -- they are individually differentiated.
Thus, for Central Asia, two indispensable prerequisites of a future democratic evolution are the avoidance of either internal or interstate wars and the continuing external pressure for reform to reinforce the efforts of domestic reformers and to achieve a more broadly based, transparent, and legitimate basis for domestic security.
A prerequisite to fostering a full understanding of mentor programs is developing a definition that applies equally to the community college setting and business or pre-college programs.
The first prerequisite to thinking creatively is the desire to think imaginatively and a good place to start that process is by noticing creative images in magazines, cartoons, TV and movies.