The flowers are radially symmetrical when the petals are arranged like the spokes of a wheel around the hub. Here are some examples:

A case which can create some problems are the flowers of Veronica, which may seem to have a radial symmetry, but are actually, albeit often weakly, bilaterally symmetrical:

The flowers are bilaterally symmetrical when there is only one plane that divides the corolla in two symmetrical halves. Here are some examples:

However, there are some cases that require a little explanation. The first case is that of the Asteraceae family, whose inflorescences, called ‘heads’ may resemble single flowers with a radial symmetry (the symmetry of the head should not be confused with that of the flowers that make it up). We have attributed the character 'radially symmetrical' to all species of Asteraceae with tubular flowers (although the heads may include strap-shaped, bilaterally simmetrical flowers along the margin, such as in daisies)…:

...whereas the character 'flowers bilaterally symmetrical' was attributed to all species whose heads have only strap-shaped, irregular flowers: