When someone says they can deadlift 500, you can assume the following:
They started with a barbell sitting on the floor;
They lifted the barbell up until they were standing up straight holding the barbell. This is called the lockout.
You can’t assume anything about what stance they used, or what grip. Some might say they deadlifted 500 when they used some sort of grip aid (eg straps, hooks) which would not be allowed in powerlifting.
For deadlifting a weight off the floor, the main variations are sumo style vs conventional, and variations of grip.
Other types of deadlift are used for various training purposes, eg Romanian deadlifts, where the barbell is not lowered all the way to the floor before lifting it again, and rack pulls, where the barbell is set at a higher position with the aim of improving your lockout on a full deadlift. Another variant is deadlifting standing on a platform, which aims to improve the bottom portion of a standard deadlift.