The processes sound really similar; I'm asking with respect to Martensite processing. Essentially the difference between Tempered martensite and Aged martensite for Steels
Although the time and temperatures may be the same, different things are happening. Tempering generally reduces hardness/strength, but improves toughness. Aging martensite is done for a group of specialty steels; PH-precipitation hardening. 17-4 PH is the most common. During aging, hardness/strength and toughness increase. Precipitation hardening is more common in metals other than steels, like aluminum. What is happening on an atomic and molecular scale needs a book to explain.
Tempering of martensite is trading strength and hardness for toughness amd ductility. Martempering is a heat treatment where a workpiece is held at constant temperature until through thickness temperature equilibrium is reached, to ensure through thickness martensite formation. Aging is elevated temperature precipitation hardening. Maraging is aging which involves the presence and maintenance of a martensite phase.
For reference, you may want to search for the terms "martempering" and "maraging". They are contractions (portmanteaus?) of martensite and the respective process name. It is worth noting these processing methods are somewhat different from traditional tempering and aging. Different enough to warrant a special name.
First a bit of background. When a steel is heated to above its A3 temperature, the iron changes phases from BCC to FCC. The FCC lattice has larger free spaces, or interstitial sites, and the carbon enters these sites, forming a solid solution with the iron. If the steel is quenched rapidly enough and to a low enough temperature, a speed-of-sound diffusionless process occurs where the dissolved carbon is trapped in the iron BCC lattice. The carbon doesnt fit well in the BCC lattice interstitial sites, distorting the latticr into an elongated BCT lattice. The BCT lattice is under high strain, which in turn causes stresses in the bulk steel, resulting in work hardening by formation of a very high density of dislocations. The dislocations are a large part of what makes martensitic steel hard, strong, and brittle. Dislocations are what allows metals to undergo plastic deformation, by gliding. Its only when there are so many of them that they get tangled up, as in the BCT distortion, or caught on the interstitial carbon atoms, that they increase strength and brittleness.
Martempering is the process of quenching a martensitic steel workpiece to below the martensite start temperature, and holding it there until thermal equilibrium, to achieve a martensitic microstructure throughout.
Traditional tempering of martensitic pieces exchanges hardness and strength for toughness by allowing dislocation density to decrease at the elevated tempering temperature. Dislocations are metastable, so they eventually work their way out of the lattice, given enough time. Higher temperatures make the process go exponentially faster.
Maraging is a special process which involves precipitation hardening. It requires large quantities of alloying elements like Ni, Co, Ti, and Mn. These elements have high affinity for carbon, nitrogen, sulfur, and phosphorus, and will form intermetallic phases given enough time at the right temperatures. Finely distributed intermetallic particles harden metals by blocking dislocation motion, preventing glide, and trading toughness for more strength and hardness. To achieve this the workpiece is quenched to achieve a martensitic structure, then aged at a slightly elevated temperature long enough for the intermetallic phases to precipitate out of solution.
Traditional aging is very similar, but does not generally involve a martensitic phase.