These two words seem to have the same translation in my native language (Cambodian). What is the major difference between these two adjectives?
For instance, you could say
By which you would mean that there is no hope that the situation could improve.
And for despair you could say:
Here "despair" is a noun. Or
Here instead it is a verb.
Comparing them for good
"Hope" is a word from Saxon origin (compare to German "Ich hoffe dass...", I hope that...). "hopeless" => "hoff[nungs]los"
"Despair" is from Old French "despoir" (nowadays in modern French "désespoir" (noun) or "désespérer" (verb)).
Taken from the second episode of The Adventure of English.
Hopeless is an adjective that means "feeling or causing despair about something;" despair is a noun (and a verb) that means "the complete loss or absence of hope."
The difference is that hopeless is never used as noun, and despair is never used as adjective.