At least not always; it depends on what one means by "bird" and "fish". Some people forget that they do not have unilateral and binding authority to define words, especially words that have already been in usage for centuries. This can particularly be a problem in the sciences, where we appropriate words and give them meanings that have, at most, a dimly suggestive connection to the original, everyday word.
For example, in physics, "force" is the rate of change of momentum, "work" is force times distance, "power" is work per unit time, and "action" is the time integral of the Lagrangian. None of these meanings corresponds very exactly to what you learned when you first encountered the words in elementary school, but that doesn't mean that either definition is wrong -- only it is important to recognize the context to get the meaning right. In a similar way, "gift" means something that is given in English, "gift" means married in Danish, and "Gift" means poison in German.
At the risk of seeming to contradict myself, though, I really do not like hearing the Ghost Hunters and others say that "spirits are energy" or earlier Spiritualists refer to anything mysterious as "magnetic". It might seem that they are doing the same thing as physicists and recycling a word for a technical meaning, but I don't think that's really what they are doing; especially in the case of "energy", it seems that they are really confusing the physics concept with the metaphysical concept of spirits, as is shown when they try to invoke the Law of Conservation of Energy. Physically speaking, what really happens to our energy when we die? Our thermal energy is lost to our surroundings, and our chemical energy is released when our bodies break down -- usually under the action of bacteria and fugi. Conservation of energy has nothing whatsoever to do with the survival of the soul. Metaphysics already has a well-developed vocabulary for dealing with such matters, and that is the vocabulary that should be used.
But back to birds, dinosaurs, and fish. Some biologists are so obsessed with kinship and descent that they want general animal names, like dinosaur, fish, or reptile to mean a group of every species that descends from a common ancestor. Since our ancestors a few million years back were apes, we are apes; since the ancestors of mammals were reptiles, we are reptiles; and since the ancestors of reptiles were fish, we are fish. It's certainly OK for them to use this kind of language among those who know what they mean, but it is wrong to pretend that any other usage is a mistake. Most people mean by "fish" a vertebrate that breathes water through its entire life cycle; this is a perfectly valid definition that excludes humans. Most people also expect a "dinosaur" to be something that is, at least in some sense, a "terrible lizard" -- and a hummingbird simply does not fit in with this definition at all.
While we're at it, there is the occasional objection to the creature that swallowed Jonah being called a "fish" in one passage and a "whale" in another -- isn't that a contradiction? There are several issues with this.
- The words translated "fish" and "whale" come from different languages (Hebrew and Greek).
- The word translated "whale" did attach itself to whales, but more generally it meant a sea-monster.
- The English word "fish" only took on its modern meaning fairly recently. It used to mean any animal that lives in water, which is how we get words like "jellyfish", "shellfish", and "starfish".