In the Pride of Our Times…
These days, they're used as synonyms, and in some cases are even defined as such. Actually, they are not.
In their original forms -- at least in the ancient Greek sense of the words -- a skeptic meant "one who goes on inquiring." It was not a naysayer, which is how we think of a skeptic today. Naysayers make snap negative judgments (from an armchair).
In modern times, a naysayer is defined as someone who denies, who refuses, who opposes something or someone, "or is skeptical or cynical," a misanthrope, pessimist, derider, scoffer, a malcontent and negativist, according to the Merriam-Webster dictionary. A skeptic is defined as a disbeliever, a doubter, and only in secondary definitions as an inquirer.
When it comes to supernatural phenomena, our Church is currently riddled with naysayers. A true skeptic is prudent, and evaluates information objectively. But in the current era a skeptic has simply become someone who likes to deny or at least cast doubt even if the "skeptic" has not conducted proper inquiry.
As one medical doctor who investigates phenomena put it, "Skepticism in the ancient Greek sense of the word is mind-expanding because a skeptic in that sense is trying not to reach a conclusion. As the popular definition of a skeptic has changed over the years to refer to a naysayer, a skeptic has become someone who denies the existence of anything that he or she hasn't personally experienced. A real skeptic is also someone who believes that the only rational means of proving truth is through the scientific method. Since truth is a moving target, I believe the only legitimate means of finding the truth is to keep searching for it."
The point (because -- actually -- there is ultimate, unmovable Truth): constant inquiry.
Tell this to those who have made judgments based on the fact that they have not experienced a grace or seen a sign when they have not left their computers to see what might be there.
The belief that one can make a snap discernment without proper inquiry is a belief founded in pride. When we are full of pride, there is no room for the truth.
It is only through humility -- lack of pride -- (and, often, fasting, plus prayer) -- that we can discern (and then, unless the Holy Spirit is there, only imperfectly).