Initially, the main thing to clarify is that shared element-traits rest on pure temperament and simple inclinations. This as opposed to more sophisticated things (values, self-expression, the fine-tuned aspects of personality) as hinted at by the individual zodiac signs. The elements work in a primal way, they describe that general "internal atmosphere" of an individual and the broad reactive patterns. If someone's horoscope reveals one element as a very dominant feature, that is usually a sure sign of having a uniform, predictable overall temperament. While the former is not unusual, most people's horoscopes display a compound of the elements, in what might be seen as a balancing act.
I'm going to use the air element as an example of how zodiac signs both differ and resemble each other within the same element. The temperament of air is what we might call a "sanguine" one, according to the ancient division. The air signs react quickly to stimuli, and have a tendency to intellectualize and verbalize all experience, even emotional such (which they typically aren't completely comfortable with). Someone with air very strong is likely to have a sunny and mostly positive temperament, even if quickly changing moods is common. They are animated and enthusing (outgoing is a defining trait). The instinctive reaction is to broaden and let thoughts and impressions flow out into the world; to handle things through communication. Accusations made against air is typically along the lines of "lacking emotional core", "easily bored", "shallow", or "unstable / unreliable".
In zodiac order, the air signs are Gemini, Libra and Aquarius. Gemini is the first, purest and simplest of the air signs. The twins are enthusiastic; nerves and reactive senses are lightning-quick in response. They need to talk about everything, to "spill it out" like a child. Gemini is the Peter pan of the zodiac - ever young, ever changing, ever careless. Immensely curious but vacillating, changing their minds in an existence defined by discovery on the mental plane. The Gemini world-view is basically an egocentric one, where the seemingly high interest in and concern for others is little more than intellectual curiosity. A way to explore the self through a mirroring act.
In Libra, the air temperament is still very present, through the sanguine temperament and the intellectualizing of all experience. In Libra however, much of the innocent, naive Gemini air-energy has calmed down and matured. Libra is focused mainly on one-to-one exchanges, on partnership, whether in a romantic or platonic sense. Libra gains self-knowledge mainly through other people, and their gentle air charm is more polished, focused and intentional than Gemini's. (Some might say artificial). The main thing that has been added to the air element through Libra, is the idea of valuing and judging things, as opposed to the simple exploratory curiosity seen in Gemini.
In Aquarius, the air element reaches its deepest but also perhaps its most sombre expression. Here the intellectual matter, maintained by the air element, expands further, and acquires a much stronger collective dimension. Aquarius takes the creative ideas of Gemini, and the relational, associative power of Libra, making large-scale abstractions and connections between different social and intellectual spheres. In Aquarius, the air energy gets impersonal and detached, lessening the importance of the self and allowing instead the idea, the cause or the group to take precedence. They are everybody's friend, but often nobody's true confidant. Aquarius is pondering and philosophical, yet tends to melancholia and emotional coldness.