According to "Buddhist Art & Architecture" by Robert E. Fisher, the stupa is one of three main types of Buddhist buildings. (The other two are the residence hall (vihara) and the hall of worship (chaitya).
Early stupas were solid inside and patterned after Hindu burial mounds. They were typically a dome set upon a low platform with a single pillar emerging from the top which had 3 umbrella-like discs covering the pillar. The pillar and it's umbrellas would be surrounded by a small fence; a miniature version of the fence that surrounded the stupa itself. The pillar represented the "world mountain" or axis mundi; the pivot of the universe. The 3 umbrellas came to symbolize the Three Jewels of Buddhism. (Buddha, Dhamma, and Sangha) Inside, the stupas were arranged into geometric, magical designs and generally housed sacred relics. Buddhist worship included circumambulation (moving clockwise) around the stupa and the sacred object contained inside.
With the emergence of Mahayana Buddhism, the practice of circumambulation was not prevalent (with Mahayanist Buddhists) as sacred items were placed in the worship hall and worshiped from the front only as the back of the hall would be blocked off for secret rituals. Robert E. Fisher notes the following regarding a change in style of stupa at Ajanta, India:
The stupa continued to be the focal point of the worship hall, and was now embellished and extended with carvings and additional motifs in keeping with the increased complexities of Mahayana worship. The body of the stupa, the anda, is moved upwards and the base extended to accommodate a large image of the Buddha. The figure is placed between richly carved pillars and surrounded by subordinate figures and elaborate, decorative motifs, typical of the Gupta taste. The pillar and umbrella at the top also gain in complexity, assuming greater prominence, nearly doubling the stupa's height in Cave 19. The once simple, earthbound stupa has evolved into a complex of images and symbols, not only attached to the earth, but also extended vertically. The older empasis upon the historical, earthly Buddha is giving way to the celestial, mystical realms of esoteric belief.
As Sri Lanka was established as a stronghold for Theravada Buddhism, a change in stupa shape (from the original Indian stupas) was noted, as in the stupa in Anuradhapura, in that the body of the stupa became bell shaped and the traditional spire became enlarged and was compared to the graceful tower of a medieval Hindu temple. Robert E. Fisher writes that "according to some" the enlargement of the traditional spire was an effort by Singhalese builders to join two symbols, the pillar of the world and the heights of Mt. Meru.
Mr. Fisher writes regarding the Sri Lankan style:
Similar proportions, the dominant bell-shaped andas, prominent harmikas (small platform with railing) and tapered spires are retained in later stupas in Burma, Thailand, and Cambodia.
Theravada Buddhism, with its more limited pantheon and emphasis upon direct action, unlike the salvationist beliefs and spectacular heavens of the Mahayana is perfectly served by the clean, uncomplicated forms and geometric harmonies of the Sri Lankan stupa.
The book notes across Asia, the stupa assumed a variety of regional forms. Thai and Burmese stupas were tall and graceful. In Vietnam and Cambodia, separate stupas rarely appeared as temples were built into mountainsides; but sometimes small "votive" style stupas were build inside those temples. In Java, small stupas decorated the terraces of the temples.
The book does go on in quite a bit more detail regarding changes in the look of stupas including the change to open, wooden stupas in the Far East, where they were called pagodas. It was also noted that later styles of stupas typically did not contain sacred relics and were not always built inside walled enclosures. They became more decorative and less sacred.
Hope this sheds some insight. :)