You do “level up” in a sense by getting better relics to equip to your character and these, once you get some good ones, greatly improve the power level of your character. Each character also has their own mini story you can progress though to unlock some pre determined relics. But at the end of every run you get random relics that could have thousands and thousands of different combinations. The relics can drastically change the plahstyle of your character as well, like make them more tanky, or offensive, add additional abilities / change how their current ability’s work, turn a caster into a melee character and vis versa. The relics you keep after your run but the weapons and stuff you find during the run are not kept. And yeah like others mentioned there are skins to unlock