Compound is King
Most any successful lifter, whether training for form or function, is likely to have a lot of the same meat and potatoes movements that you see at the core of any well structured resistance training program. Both camps do a lot of squatting, pressing, and pulling. The obvious difference is that a powerlifter must be proficient in the specific variations relevant to their competitive performance: the barbell back squat, bench press, and deadlift. A bodybuilder has more freedom to decide which variations on these basic movement patterns work best for their physique development. However, it just so happens that those competition powerlifts are also staples in the programs of a huge number of bodybuilders. As well, bodybuilders typically include substantially more upper body pulling than powerlifters.
Accessory Work for Weak Points
Both bodybuilders and powerlifters understand the need to address weak points during training. For a powerlifter, that means developing strength and muscle mass in those muscles which are preventing them from lifting more weight on the big three. For bodybuilders, it means attacking a lagging body part with extra volume so it doesn't look disproportionately small on stage. This type of isolation work is valuable for both parties.
For example, a lot of powerlifters do isolated tricep work to improve bench press lockout strength. Meanwhile, a bodybuilder might perform a greater volume of the very same exercises because their triceps are underdeveloped. Either way, the way this is addressed in training is often similar. Granted, powerlifters will include variations of the big three which help address these weak points as well (e.g. board pressing), but that doesn't mean they always eschew the method that is traditionally considered a bodybuilding practice.
What Factors Determine Strength?
If you haven't already read this great article by Greg Nuckols, then I highly suggest you check it out. It outlines the major factors that determine how strong you are with respect to a given movement. You know what the most important factor is long term? It's muscle mass. That is to say, a good chunk of a powerlifter's training time should be spent building a sufficient amount of muscle mass. This isn't to suggest that higher loading doesn't contribute to building muscle mass, but that higher volume training focused specifically on building muscle is functional for a powerlifter.
A decent amount of the time, though far from always, the arrangement looks more similar than it might sound when you really analyze things. However, the viewpoint they take to arrive at this final arrangement is reversed. Let me explain. If a bodybuilder has a day devoted to leg training, then they are likely to start with some squat variation. Obviously there are plenty of exceptions to this, but it is very common. The reason being that squats are one of the most complete leg development tools, and one of the best suited exercises to heavy loading. Other movements done for the day are meant to complement the areas that squats don't adequately develop on these lifters. To shore up these weaknesses in physique, they might do hamstring curls if their hammies don't respond to squats as well as their quads or glutes, for example. Thus, the day looks similar to what a powerlifter would structure for a day focused on developing the squat. For the powerlifter, they arrived at their training arrangement by thinking "The squat is one of my competition lifts, so I should prioritize it, then perform accessory movements that improve this lift." For the bodybuilder, their training structure resulted from thinking "The squat is one of the best developers of leg mass on the planet, I should start leg day by performing some squat variation, then hit my weak points with other supporting lifts."
Contest Preparation
This period of time is when the most marked differences in training will be apparent. A powerlifter should spend more time training at a higher intensity when approaching competition so that neurological improvements can be maximized before stepping onto the platform. If a powerlifter structures their training like many other athletes, that is, transitioning from general to specific as competition approaches, then a large amount of time will be spent training like a bodybuilder. However, that new found strength can only be fully realized by implementing maximal loading.
Conversely, a bodybuilder doesn't give two shits about his performance when he steps on stage. He cares only about maintaining as much muscle mass as possible. Training will remain more similar to the offseason, except there is typically a higher volume of cardiovascular exercise and lower volume of resistance training due to the caloric deficit they must impose upon themselves to reach competition level body fat.
The Split
The way training is arranged throughout the week is noticeably different for powerlifters and bodybuilders, but the differences are more superficial than it appears at first glance. Bodybuilders typically have days devoted to training a given body part, such as a back workout or a leg workout. Powerlifters tend to focus their arrangement of training based on the movements they want to improve. Honestly, each method makes quite a bit of sense for what they are trying to accomplish.A decent amount of the time, though far from always, the arrangement looks more similar than it might sound when you really analyze things. However, the viewpoint they take to arrive at this final arrangement is reversed. Let me explain. If a bodybuilder has a day devoted to leg training, then they are likely to start with some squat variation. Obviously there are plenty of exceptions to this, but it is very common. The reason being that squats are one of the most complete leg development tools, and one of the best suited exercises to heavy loading. Other movements done for the day are meant to complement the areas that squats don't adequately develop on these lifters. To shore up these weaknesses in physique, they might do hamstring curls if their hammies don't respond to squats as well as their quads or glutes, for example. Thus, the day looks similar to what a powerlifter would structure for a day focused on developing the squat. For the powerlifter, they arrived at their training arrangement by thinking "The squat is one of my competition lifts, so I should prioritize it, then perform accessory movements that improve this lift." For the bodybuilder, their training structure resulted from thinking "The squat is one of the best developers of leg mass on the planet, I should start leg day by performing some squat variation, then hit my weak points with other supporting lifts."
Stop Being Assholes
One person's reason for lifting weights doesn't have to be the same as yours. You should learn from others; as Bruce Lee said, "Adapt what is useful, reject what is useless, and add what is specifically your own." Both powerlifters and bodybuilders can learn from one another. Both camps can, and should, implement training that is typically associated with the other group, but the relative distribution of these forms of training will certainly be different. If you can't accept this, and you disrespect others with different goals simply because their goals don't appeal to you, then you're not a bad ass. Rather, you're a douche bag. We're all brothers and sisters in iron. Stop hatin'.