Masocore is a portmanteau of masochism and hardcore. It refers to a particular subset of platformers that require nearly pixel perfect execution, most famously 'i want to be the guy'. Think like what bullet hell is to shmup, masocore is to platformer.
Soulslike refers to games that closely follow the design of FROM software's souls series of games. They are usually third person action games with a checkpoint system, a resource cost associated with dying, a stamina system, a very purposeful set of animations, and some visual language for being able to observe or predict danger before it befalls you. Like 'Roguelike' before it, the term evolved (or devolved depending on who you ask) from referring to games using all similar systems into anything using one or more similar systems.