I understand that you are concerned with the change in color of your pup's stool from brown to brown on the inside but black on the outside.
The color of a dog's stool is variable but is influenced by what they eat as well as their ability to metabolize the food that they eat, and the metabolic wastes that their body produces. Metabolic wastes can be influenced by organ disease, gastrointestinal parasites, as well as the bacteria population living in their gastrointestinal tract.
Is she having other symptoms such as eating plant material or getting into something she should not have (cat litter box, garbage)?
Any changes in stool consistency, weight loss, increase in water consumption, or lethargy?
If she is eating and behaving normally I am less concerned with her stool color.
I understand that did have an episode of vomiting yellow, and that she has a history of disc disease.
The yellow color to her vomit tells me that she had bile refluxing from her small intestine into her stomach which she vomited. While this isn't normal, it is seen often with severe gastrointestinal upset which leads to abnormal gastrointestinal motility and bile reflux. If this is a one time event we don't worry too much, dogs being dogs do eat things and give themselves an upset stomach here and there.
Is she currently taking any medications? Drugs to control pain with disc disease can lead to gastrointestinal upset and minor stomach and intestinal bleeding. Once they are off the drugs the gut often returns to normal. But chronic use of steroids or nonsteroidals (Carprofen, Meloxicam or Deracoxib) can lead to liver disease too. If she has been on medication long term she should see her veterinarian and have some blood work checked.
If she has had a change in diet that can change gut bacteria and that may be entirely to blame change in stool color.
If she seems perfectly normal otherwise then you can try taking a wait and see approach, or adding probiotics like Fortiflora or Proviable, or Benebac to re-establish normal gut bacteria levels and see how she comes along.
The short answer is maybe, a change in the color of her stool could be cause for concern.
But the level of concern will depend upon what other symptoms he is displaying, the consistency of his stools, aa well as the color of her stool (I would be more worried if her stools were black and tarry) as to how concerned we need to be and whether this change persists.
I would mention her change in stool color to her veterinarian, and I would recommend taking a fresh stool sample into her veterinarian so that they can send it out to the laboratory for more thorough parasite checks if this persists. In clinic testing can miss some of the more unusual parasites.
I would also recommend an examination if she is developing other symptoms.
Please let me know if you have any further questions.