Taylor expansion of e in v about point, truncated after order n: taylor(e, v, point, n).
v is the expansion variable, not a binder: unlike _Derivative's or _Integral's variable it appears free in the result, which is a polynomial in (v - point) — the same role the output variable plays in _Laplace. It is nevertheless kept out of children and carried through rebuild, so substitute cannot rewrite the variable the expansion is taken in.
eval builds the series with taylorSeries and evaluates the result, so a bound v folds the polynomial to a number while a free one leaves it symbolic. It stays symbolic when n does not reduce to an integer in 0 .. MaxTaylorOrder, or when some coefficient cannot be differentiated (Gamma, fact, ... — see hasDerivative).
maclaurin(e, v, n) in the grammar is sugar for taylor(e, v, 0, n) and prints in that form, exactly as log(x) prints as log(x, 10).