항상(hang-sang, hangsang)
Always; indicates something that happens very frequently or all the time
When to use
habit expression, daily routine, frequency emphasis in negatives
The nuance
항상 is used for habits, repeated actions, or unchanging states. It fits naturally with negative sentences too.
가끔(ga-kkeum, gakkeum)
Sometimes; indicates something that happens occasionally or rarely
When to use
rare actions, irregular events, expressing rarity in affirmatives
The nuance
가끔 is used for actions or events that do not happen often. It is suitable for expressing rare frequency in affirmative sentences.