1. Distinctio ex natura rei (everyone, including Aquinas and Scotus, use this one without defining it)
2. Distinctio realiter:
a. separability criterion (Giles of Rome)
b. in subject prior to intellective operations (Thomas of Sutton)
Note that this is just from the Aquinas' followers, Dominican and Augustinian. I'll post more later on the Franciscans.
Thomas de Suttona, Quodlibet III q. 1 (ed. Schmaus 342):
"Unde haec est differentia inter distinctionem realem et distinctionem secundum rationem quod illa, quae distinguuntur realiter, habent in se subiective suam realem distinctionem, sicut patet de albedine et dulcedine in lacte. Sed illa, quae distinguuntur secundum rationem in aliqua re, non habent in illa re tamquam in subiecto suam distinctionem secundum rationem, sed solum tamquam in obiecto. Illa autem distinctio secundum rationem est in intellectu distinguente ut in subiecto et per comparationem ad intellectum, in quo est distinctio realis. Sed distinctio secundum rationem dicitur per comparationem ad obiectum, circa quod ratiocinatur."
Translation:
Whence this is the difference between a real distinction and a distinction according to reason: that those things, which are really distinguished, have subjectively in themselves their own real distinction, just as is clear regarding whiteness and sweetness in milk. But those things, which are distinguished according to reason in some thing, do not have in that thing just as in a subject their own distinction according to reason, but only as in an object. That distinction according to reason is in the intellect distinguishing as in a subject and by comparison to the intellect, in which there is a real distinction. But a distinction according to reason is said by comparison to an object around which reasons.
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