"Upon receiving..." or "When receiving..."

Practically-speaking 'when' and 'upon' are usually used to mean the same thing.

When you get the parcel... means, effectively, the same as On receipt of the parcel...

But they are not the same.

When (in reference to a definite actual occurrence or fact) means at the time that, on the occasion that. (OED)

Upon (often shortened to 'on') means Immediately after; following on" (OED)

So ...

The postman may ask you to sign for a parcel when it is delivered to you. You, on the other hand, upon receipt of the parcel, may phone in due course to let your friend know that their parcel has arrived.

As @Dan's answer suggests, upon should be interpreted as after, and when should be interpreted as at the time.

I'll give an example that might highlight the difference between the words.

When receiving a gift from foreign dignitaries, you should take great care to admire the wrapping paper and delicately unwrap the present.

Upon receiving a gift from foreign dignitaries, and pleasantries exchanged, the gift should be logged in the gift register.