One day I was having a conversation with an acquaintance about gaming and he stated that
The game has a really good lore, but not much attention has been given to the story
So what exactly is the difference between the two?
Particularly in role playing games or any game that takes place in a made up universe, the lore typically refers more to the backstory/history of either your character or the game world, while the story refers more to the current events of the game and the various exploits your character undergoes.
For example, in the Halo franchise, the different missions you go on in Halo 3 – the narrative given around them, the dialog among characters during those missions, the cutscenes that take place and such – all comprise the story of that game's campaign. But the broader picture of why you're doing that stuff, and the backstory around, for example, how it is that the Master Chief is so much taller and stronger than all the other humans, is all part of the game's lore. Some of that lore is explained through the narrative of the first two Halo games and opening cutscene(s) of Halo 3, and some of it comes from what you actually did as part of the campaign in those past games – which is to say that yesterday's story is part of today's lore.
This can be kind of confusing because "story" could be considered a synonym for "lore," but I suspect this is the distinction your friend was trying to draw.
So if some game has good lore but "not much attention has been given to the story," that may mean that lots of quality past updates have contributed to a rich history around the game universe, but recent updates haven't contributed to that history much (or at all). For example, in an RPG, maybe a recent slew of updates all focused on balancing, quality of life improvements, and adding new boss monsters to fight so players have fresh, challenging content, but no quests that advance existing storylines and expand on the game's backstory have been recently released.
lore – the history of the world
story – the actual events which occur in the narrative
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