Is this grief?

When my parents died Dad in 2000 and Mom in 2005 I mourn their passing. The 2 people that had shared my childhood were now gone. Not having sibling growing up there were no other people in the world that knew the story of my have been 'chosen'. Adopted to those uninitiated. But the thing was we had lived apart longer than together. In fact they lived in Florida longer that I lived with them. Taking in to consideration I was adopted when I was 3 and flew the nest at 18, it was a mere 15 years. And as much as I loved my parents we were not close. 
So when Dad died it was a whirlwind of getting down to Florida and helping Mom out. The arrangements had been made years in advance. And although I knew she missed her life partner of some 50+ years my mother did not break down. I left feeling sadden by the fact that I didn't know my father well or my mother. Time had pulled us apart.
When I returned to VT I could almost pretend my Dad was still alive down in Florida. I had never seen his body. So it was a mental exercise in denial. Eventually the pain of loss decreased along with the increase in the reality of his death. I cried but there were no daily reminders for me to see of him. No comfortable chair, no magazine set aside but not read, no toothbrush in the bathroom. Just pictures of happier days.
My mother lived with us for several months before she died. She died in local hospice care. And before that for a brief time she lived in assisted living. Again because of who we were and the short time living at my house there were no reminders. We knew her wishes of cremation and since our small family is far spread and I am not a great believer of wakes or funeral services my mother's passing was noted only by a small group of friends and family. I think she would have wanted it that way. It did take 3 years for me to finally be able to take her ashes to Florida to be put in the small vault with my father's remains. It was at that moment I knew great grief that the two people in the world, that had know and loved me as a child were really gone. I could no longer deny this fact. I couldn't wait to get out of Florida and never go back. Somewhere in the back of my mind they are down there and they are happy. And that is what counts.
You may ask why I bring my parents up. Well it is in connection with the recent death of my dog Gracie. I wasn't 'heartbroken' when my parents died (I do not care for euphemisms concerning death). I missed them greatly and shed many tears and I still miss them but now with a warm fondness. But my heart did not feel like it was breaking nor did I feel grief stricken. I feel these terrible emotions with the death of my dog. 
When I called my parents and told them I had breast cancer I was told I would be alright. No problem, modern science, etc. I don't remember phone calls to see how I was doing or even a card. It's not that they didn't care they just didn't understand. What they didn't understand was my fear. They were in Florida and could see it or feel it. I was 45, they were in their early 80's dealing with the death of friends, family and their own health issues, their own fears.
My dog was with me the whole time. Soaking up my tears, laying in bed with me when I felt like crap, listening to me rant about the unfairness of it all, keeping my secret fears, secret. I shared with her the things I would not share with my husband or children. And life continued on. 
With Gracie I can still see her on my bed, hear her nails clicking on the floor. The house is quiet without her joyous bark on my return home. I feel like there is an empty spot larger than me within me. Max our last dog, is a lovely old boy. But he is not Gracie, in looks or temperament. He is Max. I just miss that damn dog and at some moments it really is a physical pain. You would have had to known her to know her gentle nature and her fierce devotion. She was 'the' dog in my life. And yes I do know it gets better and there  have been a couple of days I have merely gotten misty eyed and not cried. But today is not one of them. I miss her, simply put. And despite all the emotional upheaval caused by having to make the decision that ended her life I would gladly do it again. It was a great 15 years, every last moment, the good and the bad. I just wish it had been a little longer.
So yes this is grief. Hurting from top to bottom. Crying, being okay and crying again. And it lessen with time. But I think once you have been touched by it, it doesn't go away. It always lives with you and makes you more sympathetic to others. It becomes part of who you are.