Snapshots capture a moment in time. Quality is less important as the value is in the memories. The moments are transient and must be captured when they happen.
Art photography, on the other hand, attempts to capture the spirit of the subject in a controlled fashion. The situation, lighting, and surroundings are carefully managed to tell a story that captures the spirit of the subject matter.
Both snapshots and art shots are critical. Art photographs can be printed in large sizes on quality media to hang on your wall as a piece of art. Anyone, even people that don't know the subject, should be able to interact with the picture and appreciate it. Snapshots tend to be of a lesser quality as they were captured in the moment. They are of most interest to the people that were there as they bring back memories of the event. Snapshots are well suited to inclusion in photo books or picture boxes where they can help to tell the story of the subject.
So, take lots of snapshots. They will only increase in personal value as time goes on. Take art photographs at significant times in your pet's life. Print them and hang them proudly for everyone to enjoy.