Both means 1.Two things or people together "I'd like both please!" 2.(used with count nouns) two considered together; the two "both girls are pretty" We is the Plural of "I" Us means 1.The objective case of we, the persons speaking "give it to us" 2.(informal) me "give us a hug" cowboy...

both of us = 我们俩 we = 我们， 咱们

"We" can mean us two, us three, the ten of us... it's simply the plural. "We are going to China" doesn't indicate how many people are going. "Both of us" makes it clear there are only two of you. "Both of us are going to China" tells me exactly how many people are travelling.

both of us = 我們兩個多 we = 我們