"Hide" vs "conceal"
Solution 1:
It's a subtle distinction, but conceal carries the implication that there's someone you are concealing it from, and hence the act is somewhat deliberate in nature.
For instance:
- The box was concealed beneath the rocks for centuries.
- The box was hidden beneath the rocks for centuries.
In the first, you understand that it was deliberately hidden, and perhaps required some searching to uncover. In the second, maybe it happened naturally, and one merely stumbled upon the artifact.
You can use both conceal and hide either way, but this is a common connotation.
Solution 2:
They're pretty much synonyms, and if you look them up, they're likely to appear within the other's definition... BUT, there's a but.
I've looked up in 2 dictionaries and found nothing, but then I checked the OALD. As stated in it, there are some subtle differences. One is that "conceal" is formal, the others are not signaled as such.
Go here, and scroll down, there's a Usage note. Hope that helps!
Solution 3:
Both can be used transitively, but only hide can be used intransitively.