What is the difference between a and an degree certificate?

There's no difference between "a" and "an" degree certificate. The choice between "a" and "an" depends on the *sound* of the word that follows, not the type of certificate.

* "A" is used before words beginning with a consonant sound (or a silent "h"). For example: "a degree certificate," "a history degree."

* "An" is used before words beginning with a vowel sound. For example: "an honors degree," "an MBA."

Therefore, you would use "a" or "an" before "degree certificate" depending on the *next* word in your sentence.