Yes, there are such things as "color profiles". But as far as I know (I own two Canon DSLRs) the Canon pictures use the sRGB format which is the default. In practice, you can tell your camera to produce both CR2 and JPEG. If you do so, you can compare the JPEG from the camera with the JPEG produced by from the CR2 by various applications. There is also the matter of the indicated white balance (but in your sample pictures, I think the problem is more an optimization of the global exposure).
As to DPP4 not supporting JPG from GIMP: when you export the JPG in Gimp, un-tick the "progressive JPEG" option in the advanced settings. If that fixes the problem, it means that DPP4 is not supporting something that has been part of the JPEG standard for about 15 years. For their defense, DDP4 is meant to process what comes form the camera and nothing else.
As to DPP4 not supporting JPG from GIMP: when you export the JPG in Gimp, un-tick the "progressive JPEG" option in the advanced settings. If that fixes the problem, it means that DPP4 is not supporting something that has been part of the JPEG standard for about 15 years. For their defense, DDP4 is meant to process what comes form the camera and nothing else.