Here is a quote from Einstein's paper published in 1905 "Does the Inertia of Body Depend Upon Its Energy-Content?". Talking about the kinetic energy (K) difference in a moving frame of reference due resulting from the emission of equal plane pulses of light of energy ½L in opposite directions:

"So we have

K0 - K1 = L {1/sqrt(1-v²/c²)-1}.

The kinetic energy of the body with respect to (ξ,η,ζ) diminishes as a result of the emission of light, and the amount of diminution is indepenent of the properties of the body. Moreover, the difference K0 - K1, like the kinetic energy of the electron (§ 10), depends on the velocity.

Neglecting magnitudes of fourth and higher orders we may place

K0 - K1 = ½ L/c² v².

From this equation it directly follows that:——

If a body gives off the energy L in the form of radiation, its mass diminishes by L/c². The fact that the energy withdrawn from the body becomes energy of radiation evidently makes no difference, so that we are led to the more general conclusion that

The mass of a body is a measure of its energy-content; if the energy changes by L, the mass changes in the same sense by L/9x10²º, the energy being measured in ergs, and the mass in grammes."

It looks like Einstein was actually talking about inertial mass and gravitational mass.