Today I lectured on the shoot, and one of the topics was inflorescence structures. Admittedly there is a seemingly large number of terms, but I am often puzzled why even so many professional plant taxonomists who otherwise know the most obscure details of plant morphology get so confused about inflorescences, because really the definitions there are much more straightforward than, say, in fruit morphology.
So here a short overview, in the form of an informal key:
Inflorescence is simple, that is unbranched
Flowers stalked, inflorescence long
Flowers stalked, inflorescence compressed
Flowers sessile, inflorescence long
Flowers sessile, inflorescence compressed
Inflorescence is branched
Main axis dominant, many side branches
along its length ... panicle
Panicle overall cone-shaped
... still a panicle
Flowers +/- on same level
... corymb(ose panicle)
Lower branches overtopping upper
Each axis has only one node with bracts,
then ends in flowers ... cyme
One side axis per axis ... monochasium
Two side axes per axis ... dichasium
Higher-order inflorescences, that is
inflorescences consisting of inflorescences
Raceme or spike of cymes ... thyrse
Higher order inflorescence of heads
Head of heads ... glomerule
Umbel of umbels ... compound/double umbel
There are perhaps a few more that I have missed, but those should be the most important terms. The take home messages here are as follows: First, plants really don't have that many options. They can have unbranched or branched inflorescences, and if they are branched they can be monopodial (dominant main axis) or sympodial. And then they can stack one type onto another, but that's about it.
Second, because there are so few possibilities, several of the inflorescence types are variants of the same fundamental theme. Racemes, umbels, spikes and heads are all very similar and easily transformed into one another, which is also why the same plant family may easily exhibit several of them. In the pea family Fabaceae, for example, there are many groups with racemes (Vicia, Lathyrus) but also with umbel- or head-like inflorescences (clover genus Trifolium). The latter are just the former with shorter axes.
Third, to communicate systematically relevant morphological information it is important to use the term that actually describes the structure as opposed to the overall impression. Just searching for those links I added above I found a depressing number of misconceptions. I'd say that upwards of 80% of the hits I found for panicle and corymb were wrong, often on the level of diagram does not fit the actual structure found in the plant that the diagram is supposed to depict, such as when somebody used Achillea as an example for a corymb (correct) and then drew... an umbel (ouch; I mean, just look at Achillea and you'll see that its capitulescence is richly and irregularly branched).