Patrick Stewart appeared in every episode; there's a discrepancy in how those two pages are counting.
Star Trek: The Next Generation aired 176 episodes. However two of those episodes, the premiere episode "Encounter at Farpoint" and the series finale "All Good Things...", were feature-length episodes. As originally broadcast, and as they're present on official home media releases, they were each about two hours long; that makes them hard to syndicate (typical network scheduling in North America doesn't like shows longer than an hour), so re-runs of each are typically split into two parts.
This is also apparent from Wikipedia's list of the show's episodes; the tables number each episode, but the series premiere and series finale each get two numbers (click to embiggen):