I've come across instances where I felt using both was just fine. The dictionary definition doesn't provide much clarity either. Could someone please clarify the differences between the two?
"Lift thine eyes to the mountains,
whence cometh help.
Thy help cometh from the Lord,
the maker of heaven and earth" (Psalm 121:1 KJV)
Whence is an old-fashioned word for where, or from where.
Hence, on the other hand, is best illustrated with a bit of algebra: X > Y; Z < Y; hence, X > Z. Hence means therefore.
"I'm sorry, but I simply ran out of time; hence, I couldn't pick up your dry cleaning for you."
"Then said they unto him, Tell us, we pray thee, for whose cause this evil is upon us; What is thine occupation? and whence comest thou? what is thy country? and of what people art thou?"
Jonah's shipmates wondered what he had done to bring the calamity of a great storm upon them. Since he was a stranger, they simply assumed it was his fault. Hence, they asked him, "Hey, from whence comest thou?" See Jonah 1:8 KJV.
As @tchrist comments, you need to consider the three sets of three:...
here, there, where;
hence, thence, whence;
hither, thither, whither
But in practice the last set are pretty dated/archaic forms in all contexts, and the middle set are normally only used metaphorically today.
Once you stop to think about the fact that the usage is metaphoric, it should become clear. Here are some written instances from Google Books...
([here is] some stated fact) hence we derive (some other fact) (i.e. - "from this fact here")
(some statement) thence we derive (some fact) (i.e. - "from that statement you just read there")
(some statement) whence we derive (some fact) (i.e. - whence=wherefrom)
You won't come across whence so often these days, but (as I hope those examples illustrate) it can sometimes be used in contexts where either or both the others would be perfectly acceptable.
Since the usages are all metaphoric, the "location" of the "statement" (or thing referenced by the statement) is somewhat uncertain. In speech/physical space, the difference between "There it is!" and "Here it is!" may simply depend on whether you're pointing a finger or spreading your hands as you speak.
But at any point within a written text, here could encompass the entire book you're reading, and there could mean just the previous sentence or clause. And where/wherefrom/whence can always refer to anything written previously (normally, the immediately-preceding statement).
To sum it all up - if you're not sure which to use, stick with the most common form (hence). If there's a strong sense of from there or from where in your context, use thence or whence.
Let's assume you know what here, there, and where mean.
Hence, thence and whence mean from here, from there and from where.
Hither, thither and whither mean to here, to there and to where.
"Whence" means "from where." It's not a substitute for "hence." Its meaning is nowhere to "hence."
Whence do you come?
It means, "from where do you come?"
Hope I answered your question.
I recommend the following sites for great grammar info: