天都山 a name of maintain, so 爬天都山 means climbing the Tiandu mountain.

I bet you must've seen the collocation “爬山”“爬…山”（加上山的名字） before. 一座大山may consist of a few peaks（山峰）, so there may be different routes to different peaks 天都峰是黄山三大主峰之一(one of the three major peaks)

黄山 consists of many mountains and 天都峰 is just one of them. A very famous one.