Now your (imaginary) dog. You get empathy from your dog not compassion. Well, I don't actually know and this is the problem. Your dog may truly believe that it is showing you empathy and feeling exactly the same as you and doing what is necessary to help and yet, you deny it. Thinking we know the feelings of a dog and its intentions is a little silly.  So this is  the same issue with believing we can hold the same position as another human.

Your wife (sounds like a saint :D ) may make you feel better about what ever troubles  you but it doesn't necessarily help the cause  of your troubles. She may have no actual value in helping you problem solve other than helping you feel better about yourself and then perhaps you can fix it but, why are we unable to emotionally make ourselves feel better? And then, now that you are feeling good, what if you are still unable to repair it and need practical help? Depressed again? Does another empathetic pat on the back help?

A compassionate person need not feel anything but can still understand that you feel something and can therefore comfort based on that. Plus, from this position they are also able to better help or find help for you. 

I think that people want to feel better, not actually improve the situation. This is why so many people can avoid their problems by immersing themselves in entertainment or vice. eventually though, a crash will come.

I think that this conflation of terms is making people confuse what is actually going on and as society keeps pushing incorrect definitions, people increasingly use two very separate terms interchangeably.

I like it when you drop by because I know you are here to discuss what is actually at hand. As you know, I like to think and write across many areas whether I hold this position in 5 years or tomorrow, who knows.