I'm not sure where the idea that a pet is the same as a familiar came from. I guess I have to blame it on some of the crop of poorly researched books on the market these days. But the fact of the matter is that our beloved pets and a Witch's familiar are very, very different things.
A Witch's familiar is an animal spirit or a magical construct created by the Witch or the Magician as an adjunct to their magical workings, as a repository for power, and if needed as a defense against magical attack from another magic user. A Witch or a magician can draw upon the energies of the familiar when they need an extra boost of energy in a magical working. Conceivably if the spell is important enough, the Witch could completely drain the familiar of energy causing it to "die" or cease to exist. And in the case of a magical attack, the attack could be diverted to the familiar so that it would be the familiar which is destroyed rather than the magic user. None of these are things that I think any of us would want to do with our pets.
There is an excellent article on familars here: http://en.wikipedia.org/wiki/Familiar_spirit
Animals are very sensitive to the energies around them and they may be drawn to us when we are working magic because they can sense the energy. They also want to be around their people, which again will make them want to be where we are..and that may be where we are doing magic. Neither of these things makes the animal a familiar or inherently magical in and of itself.
On the other hand, it is possible that this bird (if it is always the same type of bird) might be your animal guide. Animal guides are very different from familiars. They generally appear to teach us some lesson we are supposed to learn.
To add to what Lark said, a familiar is merely a spirit friend or assistant in a way, and can be anything, not just an animal. In fact, most familiars are not animals. I do however find that cats are natural mediums and this may be why cats were commonly viewed as the witch's familiar. Kindred spirits are usually confused or used interchangeably with familiars.
Those that are created (thoughtforms/egrigore) are soul-less spirits.
When a witch draws energy from a spirit, if drained entirely, the spirit doesn't truly "die" but sleeps in a way until their energy naturally rebuilds or the witch heals them by replenishing the taken energy later. I know Lark knows this, but I can see where so many may take that the wrong way. Spirits can't die!!! No slaying spirits please, that's for RP.
Thoughtforms are commonly destroyed and recreated, and truly should be, or else they can become hard to control and tainted. Drawing from their energy and restoring it later would keep the created spirit the same but constantly renewed so that it would not go sour.
