Maximum is used to express sort of limit while maximal is a technical and scientific term

To me, maximum used and adjective and maximal mean much the same thing. However I very rarely hear maximal used in general conversation. Maximal is also a technical term used in mathematics and there is a discussion of its meaning here: https://en.wikipedia.org/wiki/Maximal_and_minimal_elements

I think there is a slight difference between the maximum and the maximal. While maximum is the 'maximum' which means there might not be something higher than that, maximal is more ambiguous. Besides that, while 'maximum' might be both a noun and an adjective, maximal is always an adjective.