山 and 丘: mountains and hills
Distinguish landform names from the endpoint of a climb.
A mountain
山 (やま) means mountain. 「山に登りました」 says the speaker climbed a mountain.
「山のふもとに村があります」 locates a village at the mountain's foot. Do not change ふもと into the summit.
A hill
丘 (おか) means hill. 「丘の上から町が見えます」 says the town is visible from the hilltop.
「なだらかな丘が続いています」 describes a series of gently sloping hills. なだらか identifies the slope's character.
Names versus arrival
Do not impose one fixed height boundary between 山 and 丘 everywhere. 「高い丘」 can describe a relatively high hill.
「山に登りましたが、頂上までは行きませんでした」 says the speaker climbed the mountain but did not reach the summit. 登る alone does not guarantee summit arrival.
Does 「山に登りました」 necessarily establish arrival at the summit?
Show the answer and why
No. An explicit extent such as 頂上まで is needed to make summit arrival clear.