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The highest = yang tertinggi (INA)
The tallest = yang terjangkung (INA)

"High" can refer to physical condition, like high mountain. And can refer to non physical condition, like high position or high rank.

"Tall" does refer only to physical condition. In example tall man, tall building. Cannot be used to show position or rank.
 
Is it not that , if you are the tallest , that you could climb a mountain better than anyone else . And if you are the highest , you won't need to climb a mountain .