Modern English, apart from a few vestiges, does not express mood by morphology: instead, it has a range of modals (such as will, can, must, should) each of which has its own range of meanings.
Some of them can be used to translate particular morphological constructions in other languages: but in my view nothing is gained by trying to put labels on the English constructions according to which modal (or none) is used.
"Subjunctive" is a case in point: in many European languages (including Old English) this refers to a particular morphological form of a verb - not to a construction. The old English subjunctive survives in a few places, notably in the irrealis conditional "If he were...".
Some people refer to some other constructions with modals such as would as "subjunctive", apparently because if they were translated into French or Latin they would be expressed by a subjunctive. I think this is obfuscatory and unhelpful.