Finger joints
I have not seen this before on any rifle stock. I think what has happened is these people are finger jointing the raw wood while it's in whatever dimensional size they have milled it down to for processing into gun stocks. The wood they use is not the same as our walnut, birch or whatever. Cost prevails and if a 30 inch piece of wood is needed for each stock anything less than that is useless. My guess is the difference in color in the photo is only because of the variation of color in that particular kind of wood. You see similar, although not as extreme, variations in pine molding that has been finger jointed. The same thing as referred to in Meddac19's post. The raw material that door company is using probably came from another source. Wherever it came from the machine used to manufacture it is set up for a standard and particularly selected size of raw material. You can't simply poke a piece of gunstock in it. If the glue is good the joint in that rifle stock will no doubt be stronger than the surrounding parent wood and would perform under the stresses of rifle use.
Now, how to do it yourself using two separate stocks as raw material. I can't think of a good simple method in the home shop. Somehow both pieces are going to have to be held in the exact same position and then cut in the exact same way to fit together tightly. Then, however that is done it has to be set up so the end result is an absolutely completely straight stock on all planes. The indexing wood lathe would work I think. I know one thing, it's not a job for an inexperienced armature. That's what I am when it comes to using an indexing lathe.
If you simply want to attach the front of one stock to the rear of another it can be done at home. The difficult part is temporally clamping or somehow hooking the two stocks exactly parallel side by side and even to some reference point, i.e., trigger guard screw hole or anything else. Build a simple jig to hold the stocks flat on a band saw table. If it were me I'd mark a single finger joint and cut away. When you attach the two pieces together the end result will be shorter than the original by whatever the kerf is on the saw blade. If the cut was made behind the inletted portion of the stock it probably won't matter. If the cut is anywhere in the inletted area you may have to glue a kerf thick spacer in the joint or if appropriate modify the inletting.
This entire post is moot as far as I'm concerned because I wouldn't go to this much trouble. There's no doubt a better way to do this. I never could figure out how to do anything the easy way. That's why I don't go in my shop much anymore.