The dictionary says both mean "to burn". Obviously there must be some difference, subtle or otherwise. What are they?
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First of all note that burn means different things in English:
Quemar is just burn, in with meaning 3. Meaning 2 will be quemarse or arder.
Prender, however, means to catch fire (meaning 1), put in flame, that is, the act of start burning. It is sometimes used redundantly: prender fuego.
For example, you can say:
But if you say
The meaning is subtly different: the former means that it is difficult to start a fire with wet wood; the latter means that wet wood does not give great flames.
But with the following phrase:
The meaning is practially the same.
Note that prender, as is, without fuego following may require some context, because this word has a lot of different meanings.
The meaning of prender as turn on an electrical device sounds regional, from America, I think.
You can use quemar and prender for the verb "to burn".
However, prender is used to "turn on" something, like:
Besides, you can use encender; so you can