Aster family flower anatomy gets complicated and the subject is full of jargon. Here’s a photo-illustrated primer.
Aster family plants have flowers by the dozens or hundreds, clustered together in heads. This plant —>
is Helenium flexuosum (sneezeweed), with one open head and one still-developing head. What appear to be yellow petals are actually individual ray flowers. If you click on the image and zoom in, you can clearly see several individual flowers at the bottom, each one three-lobed. The purplish, nearly spherical center part is composed of disk flowers. The ones on the bottom half are open, with two-parted stigmas protruding, while the upper half holds still-closed buds.
“Ray flower” is a general term. There are actually two different types of rays: ray florets and ligulate florets. Both are tubular-shaped at the bottom, and flatten out towards the top. Ray florets can be sterile or pistillate (that is, female*), and have 2 or 3 teeth or lobes at the end, Ligulate florets are perfect (that is, bisexual: containing both male and female parts*), and often have 5 teeth or lobes.
Smallanthus uvedalia (large-flowered leafcup), showing 10 ray florets and 13 open disk florets
[click on the picture to zoom in and see the details]
The central flowers in a head are called disk florets. These consist of five petals fused together, so that they look like a single five-lobed tube; the stigma often protrudes, sometimes dramatically. The central disk can be more or less flat to almost spherical (as in the first photo).
next time: the three types of aster flower heads
*with apologies to my friend Linda for anthropomorphizing