희망하다(hui-mang-ha-da, huimanghada)
To have a wish or desire for something; to hope
When to use
Expressing future wishes, Wishing for uncertain outcomes, Formal expressions of hope
The nuance
희망하다 is mainly used to express wishes or desires, often for uncertain or distant future outcomes.
기대하다(gi-dae-ha-da, gidaehada)
To believe or anticipate that something will happen
When to use
Anticipating likely events, Expectation based on belief, Everyday expressions of anticipation
The nuance
기대하다 indicates a mental state based on belief or anticipation that something is likely to happen.