If it’s on weapon, it applies only to attacks with THAT weapon (in case if dual-wielding or using a shield). Aside from that, they’re equal.
If it’s on proc, then you may see in proc description, when it triggers. If it’s on item itself, then it triggers on weapon attacks (any skills that use %weapon damage).
Only “weapon” part (=% weapon damage). Of course, it it’s a stat on item or buff - stats on skill itself benefit WHOLE skill.
Piercing damage will be added as “non-weapon” part (it’s same for any other similar skill, too). Only “weapon” part will benefit from varios weapon-related effects, such as resistance reduction.
If you dont use skills, that deal “% weapon damage”, or they deal not enough of it, then, your bet is various skills (like Curse of Frailty or Thermite Mines), or constellation procs (Manticore, Solael’s Witchblade, etc), or item procs (Exterminus, Warpfire, etc.).
If you mean constellation stats (like resistance reduction from Viper) - then YES. But if you mean constellation procs (like Solael’s Witchfire), then NO. Constellation procs are considered skill’s effects, and will trigger with any related skills, not just weapon-based. Even skill that dont inflict damage at all(CoF) will work.
Do note!
If skill deals less than 100% weapon damage, then all “weapon-related” effects will be penaltized appropriately (so if it’s 50% weapon damage, and you have 20 reduced resistances, you will reduce only 10 resistances with that skill).