This was conjectured by Witten in his paper in his paper Monopoles and four-manifolds. The conjecture says that if $X$ has Seiberg-Witten simple type (meaning that $SW_X(\mathfrak{s})$ is nonzero only when the moduli space associated to $X$ is 0-dimensional) and satisfies some mild homological conditions (including $b_1(X)=0$ and $b^+(X)>1$ odd), then $X$ has Donaldson simple type, its Donaldson and Seiberg-Witten basic classes coincide, and its Donaldson series has the form
${\mathcal D}^w_X(h) = 2^{2+(7\chi(X)+11\sigma(X))/4}e^{Q(h)/2}\sum_{\mathfrak{s}} (-1)^{w^2+c_1(\mathfrak{s})\cdot w} SW_X(\mathfrak{s})e^{c_1(\mathfrak{s})\cdot h}$
where $\mathfrak{s}$ ranges over Spin^c structures on $X$ and $Q(h)$ is the intersection form on $X$. Recall that the Donaldson series is defined as a formal power series by the sum $\sum_i D^w_X((1+\frac{x}{2})\frac{h^i}{i!})$, where $x$ is a point of $X$ and $h$ is an element of $H_2(X)$; this definition is originally due to Kronheimer and Mrowka, in Embedded surfaces and the structure of Donaldson's polynomial invariants.
There is a series of papers by Feehan and Leness proving many cases of the conjecture, although it has not been established in full. For an overview of this program, originally proposed by Pidstrigach and Tyurin, you might try their survey article PU(2) monopoles and relations between four-manifold invariants. Notably, their most recent paper, Witten's conjecture for many four-manifolds of simple type, proves it assuming that $c_1^2(X) \geq \chi_h(X)-3$, and before that, A general SO(3)-monopole cobordism formula relating Donaldson and Seiberg-Witten invariants was used by Kronheimer-Mrowka to prove enough cases of the conjecture to establish the Property P conjecture, in Witten's conjecture and Property P.