Question: It seems that *I slept during the holiday* can be translated into two ways:

> 
> Mi dormis *en* la festotago.
> 
> 
> Mi dormis *dum* la festotago.
> 
> 
> 

Do they both mean the same?

Answer: 
Your two sentences mean different things.

*Dum* implies duration. *En* suggests that something happened within the period.

* Mi dormis en la festotago.

At some point you slept.

* Mi dormis dum la festotago.

You spent your festival day sleeping.
PMEG has a paragraph about this. <http://bertilow.com/pmeg/gramatiko/rolmontriloj/rolvortetoj/lokaj_rolvortetoj/en.html#i-sb8>

*Dum* shows a duration (over which the action took place).
*En* can show one of two things

* a **point** in time
* the time needed to complete an action, basically the **point** in time when the action will be finished.

You can also have temporal *tra* and *por*.

*Mi dormis tra la festotago* - almost the same as with *dum*, but with emphasis on sleeping *through* the whole period. 

*Mi ripozis por unu tago* - I took a break which lasted one day.