As a game developer, I strongly disagree with Rathony. The question asks about two words that are, for the question, written in English. That is as far as it goes.
The two words are common in that they are contextually in English, but they are in fact jargon. They mean the same thing in any language or interpretation. They are very familiar terms in the profession of game development, and just as familiar in programming.
However, they are as on topic in gaming as cheat codes or exploits.
Both terms reference a general reason in which the game behaves unexpectedly. The layman easily explains them as the same, but any programmer worth their weight will quickly explain the difference. this difference is explained well in current answers.
From the gamers point of view, this differentiates how said exploit can be interpreted. For example, there is a glitch in Spyro: Enter the Dragonfly that allows you to jump to the other side of an important waygate earlier than intended.
This means the player can access content early. By definition, if they s was a bug, they would likely be unable to access it at all.
It's a tricky comparison, but they both have merit as video game terms. Both words are thrown around a lot in game guides.
As such, it would be very useful for the typical gamer to know what each means;
Take another example. I am trying to achieve a bugged achievement on Xbox title B. Does that mean the achievement is known not to work/unlock, or can I achieve its requirements through unintended advantage of the specific way the game is made?
One definition tells me to not waste 5 hours trying. The other tells me there is a trick the doing it in 30 minutes.
While not inherently a gamer term, the question in itself has the potential to give the gamer knowledge to strategically decide their course of action, no matter what the game.
This question should be promoted, not removed