位置 and 地点: an object's position and an activity point
Compare a location marked for an object with a point used for departure or measurement, retaining the stated activity and result.
Where an object is positioned
位置（いち） refers to a location or position. 「地図に避難所の位置を赤い点で示した。」 describes marking the shelter's location with a red dot on a map. The shelter is the object whose position is shown.
「机の位置を窓の近くへ移した。」 describes moving the desk to a position near the window. The object and destination are stated; its exact previous position is not.
A point used for an activity
地点（ちてん） means a point or location. 「出発地点に全員が集合した。」 says that everyone gathered at the starting point. 出発 identifies the role of that point.
「橋から百メートル離れた地点で測定した。」 says that measurements were taken at a point one hundred meters from the bridge. 地点で locates the measuring activity; it does not state the measurement result or precision.
Position and the role of a point
The 位置 examples locate a shelter or desk. The 地点 examples identify points for departure or measurement. The word 地点 does not itself require coordinates to be given.
One place can be described as an object's position and as a point used for an activity. The object and activity explain the difference without making the words exclusive classes of places.
What does 地点 identify in 「出発地点に全員が集合した。」? Has everyone already departed?
Show the answer and why
It identifies the starting point where everyone gathered. 集合した states that gathering occurred; it does not state whether everyone subsequently departed.