In math, I was taught to always be mindful of the definitions-particularly because they change on context. When studying certain systems different conventions make sense than in other studies. It’s not a judgement call as to what matters absolutely, just what helps the area of study the most. Further, the better flexible you are with working across contexts the better a grasp on the topic you have. (So further, the more ways you can explain a concept or prove a theorem the better you understand the concept.)