My understanding is that most spells have verbal ("levio-sAH") and somatic components ("swish-and-flick") but that all elements of the spell's casting sort of add power to the same pot. So some very basic, simple spells can be performed without one or the other of those because the caster has the rest of the spell so dialed in.
It seems like the words and actions aid in successfully casting spells, but skilled wizards can make it happen without the full recommended set of actions. On Pottermore, Rowlings writes about Native American and African wizards being more skilled in completely wandless magic (the wand being a European invention), so presumably they have just learned to rely more heavily on words, or on the mental process, etc.
The most glaring difference between magic practised by Native
Americans and the wizards of Europe was the absence of a wand.
The magic wand originated in Europe. Wands channel magic so as to make
its effects both more precise and more powerful, although it is
generally held to be a mark of the very greatest witches and wizards
that they have also been able to produce wandless magic of a very high
quality. As the Native American Animagi and potion-makers
demonstrated, wandless magic can attain great complexity, but Charms
and Transfiguration are very difficult without one.
and on African wizards:
The wand is a European invention, and while African witches and
wizards have adopted it as a useful tool in the last century, many
spells are cast simply by pointing the finger or through hand
Of course, these are specifically about wand use, rather than verbal vs somatic components specifically, but I think we can probably extrapolate and say that the wand would be a pretty important part of the somatic component for a wizard trained in its use. Presumably a similar thing may follow with the spoken word: maybe they just think it instead and that's enough.