From the greatest fountain of human knowledge ever constructed: Wikipedia.
(All of science is a very close second.)
Some logicians, however, draw a firm distinction between a functional form, like those in the left column, which they interpret as an application of a function to a pair of arguments — and thus a mere indication that the value of the compound expression depends on the values of the component expressions — and an equational form, like those in the right column, which they interpret as an assertion that the arguments have equal values, in other words, that the functional value of the compound expression is true.(Source)
If we’re picking sides, put me down for functional. I’ve never met an equivalence in the wild, except for functional ones.
Besides, even an assertion is a type of function, a flow.
Anyway, here’s my go at it 😉