Gaoxing (高兴) vs. Kaixin (开心)
高 = highly; 兴= delighted
高兴 = happy; glad; delighted
describe a  emotional state of being delighted

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开= open; 心 = heart
开心 = happy; joyful
metaphorically describe an effect of being happy

Both 高兴  and 开心 means 'happy', but with different emphasis.
For example, if you are glad that you didn't get killed in a car accident, you can say: &quot;我很高興我還活著&quot; (I am glad that I am still alive), but you wouldn't say: &quot;我很開心我還活著&quot; (I am joyful that I am still alive)
Another example,  We use 我很高興見到你 (I am glad to see you) as a polite greeting, but &quot;見到你我很開心&quot; (seeing you make me happy) would be a more passionate expression.

开心 is also more personal, e.g. &quot;今天是我最开心的一天&quot; is more natural than &quot;今天是我最高興的一天&quot;


Another word for 'happy:
快 = satisfactory; 樂 = delight
快樂 = happy/ joyful/ cheerful (describe a joyful emotional state). It can be a noun or an adjective