What is the difference between them?

1) How do you distinguish between a lie and the truth?

2) How do you tell whether a lie and the truth?

Question

What is the difference between them?

1) How do you distinguish between a lie and the truth?

2) How do you tell whether a lie and the truth?

Answer

The first one is grammatically correct, but the second one needs some changes:

How do you tell whether something is a lie or the truth?

The meaning is similar, but the first one is a little more formal.

Answer

They have similar meaning.
You can also say “distinguish lies from truth” or “tell whether it is a lie or the truth”.

Answer

As Jonathan said - the second one needs adjusting but to me they are the same. I hope it helps.