Btw, as of 2010s-2020s, there apparently appears a reasonable line between the two classes.
While the "role one"(destroyers are tilted to actively participating in the Airsea battle, frigates are more of GP/ASW combatants) is mostly true - it is only that "mostly" true, for there are quite a few AA frigates.
Other lines - cell numbers, for example - are reasonable, but blurry, with a large intersection around 48-64 cells.
There is, however, one line, which really kinda works in almost all cases - it's the presence of "heavy", very-long range, SAM complex, with SAMs so large that they are becoming fully-capable multipurpose weapons: with multiple modes of guidance(ARH/IR/GPS), warhead weights approaching 100kg mark, and ranges(against surface and land targets) exceeding 500 km - they're becoming very reasonable weapons of choice against essentially all non-submarine targets, be it ship, plane, or even a bunker.
Those are ships with strike length Mk.41(SM-6) or with HQ-9, as opposed to much lighter, <500kg, ~150km/less class weapons(PAAMS with Aster-30, Redut with 9M96E, Tactical length Mk.41 - ESSM/SM-2, HQ-16) with relatively small warheads of around 20kg.
This doesn't mean that heavier ASCMs are redundant now - but their relative advantages on ships with such SAMs have eroded substantially; for light ASMs(Harpoon, NSM) - it's essentially gone.
Frigates, on the other hand, are clearly sticking with those "medium" SAM systems. Those have managed to achieve very competitive ranges for relatively light missiles, but - unlike heavier weapons, warhead weights, among other factors, ensure the absolute need for a separate anti-ship/land attack strike system. The number of missiles for a separate strike system is inherently limited(but it slowly rises - it will reach 24 on new RN and RuN frigates), so it remains reasonable to ensure the largest possible oomph per missile.
This, as always, isn't a rule set in stone - we aren't in the era of naval treaties, after all; but as of now I can only come up with only one recent exception - the Daring class, and it isn't that much of an exception, to begin with: firstly, even during the WNT times, Atlanta class wasn't a destroyer regardless of her caliber; furthermore, even if Darings use lighter missiles than typical for a destroyer - their AA outfit is still clearly separated(and superior) compared to the corresponding type 26 destroyer.