Record of Lodoss War itself was originally a tabletop game that took place in the 80's and had its campaign logs published in a Magazine. It was very different, for example Deedlit's player was a dude and there was no romance between her and Parn, in fact the only thing she wanted from him was his fancy magical sword so she could sell it for a lot of money, and would use everything from trickery to seduction to attempt to get it from him. Another is that Ghim's player simply ducked out of the game with little warning, which is why he dies in the novelizations of the story.
The setting, which was later made the officially setting of a Tabletop RPG called Swordworld (The original games used D&D 1E and other systems), was used in three major campaigns that were published in those Magazines:
Parn's Party: This is covered in the OVA series for the most part
Orson's Party: This is a bit odd, it was at least partially covered in both the OVA series and the Anime series, so there is some plot overlap between the second half of the OVA series and the first part of the Anime
Spark's Party: Covered in the second part of the anime
Honestly your best bet is to just watch both since both cover stuff the other doesn't, and both are really weird for sort-of covering Orson's campaign but not quite.