Primarily the passive.
Bruisers are tanky, but are not actual tanks (for the most part). Obviously there's some overlap, with some bruisers being able to fulfill the tank role and some tanks able to build and act as bruisers.
Anyway, DMP is a bruiser item because the stats it gives are tanky and the passive is intended to help close the gap (while being susceptible to cc) and deal some extra damage. Basically it brings both damage and tankiness to the table, which is what bruisers do. Abyssal sceptor is a common item for AP bruisers, since it brings both MR, penetration, and AP to the table. You'll often see more short-ranged AP and AP bruisers alike build things like RoA and Zhonyas rather than Luden's Echo for similar reasons.
Anyway, to help differentiate the two types of items and where they intersect (and dear lord there's quite a few overlaps that make this goddamn confusing, looking at you Randuin's) is items like Frozen Heart or Righteous Glory. Items with passives that serve to aid the team (lowering enemy dps, and strong engaging) that can be decent on a bruiser, but most definitely scream tank. DMP only speeds on champion up, and the passive requires an aa, so it's probably stronger on a bruiser who's going to aa anyway (Garen, Darius) rather than a tank who'll probably open up with a spell (Amumu). Obviously there's cases where DMP might be good on a tank, but sometimes RG or other things do that job and better.
Man, did not mean to type monster paragraphs... a shorter way of saying this is that tank items tend to bring more utility to the table for the team with a more defensive focus, and bruiser items tend to aid the champion individually and deal with a hybrid of tankiness (which does not always equate tank) and damage. There's a lot of overlap, with Randuin's Omen and Warmogs being strong items for both classes, which I suppose makes sense because bruisers and tanks themselves often have a bit of overlap as well.