A scheme is equidimensional iff all its irreducible components have the same dimension.
A ring is tell equidimensional iff all its minimal primes have the same dimension (that is $\text{dim}(A/\mathfrak{p})$) and all its maximal primes have the same codimension (height).
For a affine scheme these definitions seem different: the dimension of irreducible components corresponds to the definition of the minimal primes. But why is there a condition over the maximal primes (codimension of points)?