The words relevant and pertinent are members of a group of words that—according to Webster's Dictionary of Synonyms (1942)—also includes germane, material, apposite, applicable, and apropos of. That dictionary distinguishes between the two words you're interested in as follows:

That is relevant which has any traceable connection, especially logical connection, with the thing under consideration and which has significance in any degree for those who are engaged in such consideration [examples omitted]. ... That is pertinent which is so decisively or significantly relevant that it touches the real point at issue or contributes materially to the understanding of what is under discussion or to the solution of that which is in question. [Examples omitted.]

I was surprised at the claim that pertinent indicates a stronger degree of relevance than the unadorned word relevant does, since I have always imagined that the two words were used for the most part interchangeably, though perhaps with pertinent more closely bound to "questions," and relevant to "issues." But when I checked the synonym discussion under relevant in Merriam-Webster's Eleventh Collegiate Dictionary (2003), I found that the same distinctions that MW made in 1942 were on offer (albeit in shortened form) sixty years later:

RELEVANT implies a traceable, significant, logical connection {found material relevant to her case}. ... PERTINENT stresses a clear and decisive relevance {a pertinent observation}.

So that's the steadfast view of Merriam-Webster. I remain skeptical about the level of real-world adherence to these distinctions in popular usage today.