From an admitted non-expert, the way I understand it is this: A roguelike is turn based, procedurally generated to some extent, has some form of time/turn crunch tied to a carried resource (food/hunger is pretty common), and has leveling involved as part of the core gameplay loop. The idea being that you try to balance out luck (with the items/equipment you find, enemies that spawn, how well you're doing in a particular combat, etc) with skill (knowledge of the game systems, knowing how to build, knowing when to cut your losses and run, when you have enough resources to gain some levels, etc.). There is also perma-death: Once you die, your run is over and you have to start fresh.
A roguelite involves some of these aspects, but plays things much looser. Typically there's some level of perma-death in that a run is over when you die, but there's also a meta-currency to allow for progress/power upgrades between runs (like increasing starting health per run by using items that have a chance to drop during a run). They are often not turn-based, and don't necessarily have the same time crunch. The similarities lie in the fundamental idea: balance luck introduced by randomization/procedural generation and skill from game mastery, and if you fail then you have to start a new run. Different folks will have different criteria for the two terms (I saw a purist say that it's not a real roguelike if it has anything other than ASCII graphics), but that's how I summarize them.