'Isms' are labels. They enable us to group theories, ideas, arguments, that have enough in common to be usefully (for some purposes) treated together. So, for example, empiricism is the label for theories &c. which assume that experience is the only source of knowledge, or the major source of knowledge, or the sole source of one kind - or some kinds - of knowledge. There is always this loose commonality, more like Wittgensteinian family resemblance than anything else. (Wittgenstein, Philosophical Investigations, I §§66-8.)
One objection to the use of 'ism' labels is that they readily suggest the opposite - that empiricism, to keep to that example, can be defined in terms of necessary and sufficient conditions : X is an empiricist if and only if ..., whereas in fact empiricism has no such nuclear, essentialist definition.
This can lead to unfruitful discussions about whether so-and-so was 'really' an empiricist. The label is not precise enough to make such inquiries helpful.
'Isms' also blot out differences. When I consider Locke, Berkeley and Hume, 'the British empiricists', I am struck by the serious and deeply significant differences between them. Not only do they not agree on what 'experience' is, they exhibit fascinating differences in style of argument, treatment of topics, levels of scepticism and so forth. I'd like to say that the blotting out of differences isn't a reason for using labels but for some folk (not all who use them) they are just that and enable a fast, undiscriminating trip through the history of philosophy.
The example you use is 'neoplatonism'. How can this be characterised ?
One distinguishes Neoplatonism from other philosophical positions
(e.g., Aristoteleanism, Stoicism, Middle Platonism, and so on) by its
metaphysics- by the primacy it gives to unity: to be real is to be one.
It is, in a word, a monism but of a unique sort inasmuch as it does not
deny the existence of the multiple - the intelligible, psychic and physical universes - but it does deny their reality. To the extent that individual existents are individual, they are unreal. Each individual is real only insofar as it is the One on a lower level. (Leo Sweeny, review of Neoplatonism and Christian Thought by D. J. O'Meara, The Review of Metaphysics, Vol. 40, No. 4 (Jun., 1987), pp. 786.)
Now, this is fair enough to 'net', to capture important similarities between, (say) Pltoinus, Porphyry, the Pseudo-Dionysius, Proclus, Eriugena. But when you descend to detail, the smooth surface of 'neoplatonism' cracks into innumerable differences about the nature of 'unity', of the 'individual', of the distinction between 'existence' and 'reality'.
Moral : the deeper one goes into philosophy the keener one is to abandon 'isms' and to look at each thinker in their own right.