Another example if we compare logographic language systems (e.g. Chinese characters, hieroglyphs ...) to alphabetic systems. I guess we can say both are text, but logographic systems are close to pictures as well (pictographic systems even more so) and they can convey information in much less characters, at the cost that one needs to know a much larger "alphabet".
Similarly if the information we are trying to transmit is actually an image, transmitting the actual image is certainly much less information than transmitting a description of the image. That is also why the comparison with the bird and twitter image falls flat. The image conveys a specific image, not the generic image of a bird. To describe that specific would need many more characters than 4. Similarly if I have a large set of numbers, it's much more efficient to store and transmit in binary format not as text.