It might help to understand the difference simply by realizing that in the first instance the English word for vision relates to the dream/oracle/revelation/vision Daniel was having and in the second instance the English word for vision refers to the vision within the vision. The distinction being between the form and the type, it took the form of a vision and he saw a type of vision.
Notice where Daniel was in the physical and where within the vision he describes himself
“And I saw in the vision; and when I saw, I was in Susa the citadel, which is in the province of Elam. And I saw in the vision, and I was at the Ulai canal.”
Daniel 8:2 ESV
In the physical body Daniel was at Susa citadel a province of Elam, he was inside a fortress but in the vision Daniel was at the Ulai canal by a long narrow body of water, out in the open and not within the confines of a fortress.
Notice where Daniel is described in v16 when the man begins to speak
“And I heard a man's voice between the banks of the Ulai, and it called, "Gabriel, make this man understand the vision."”
So the voice is speaking to him from within the vision בחזון while Daniel is having another vision המראה inside of this vision בחזון
It may help if I inaccurately over simplify it - Daniel was dreaming and he saw a vision. But because it wasn’t a regular dream in English (I’ll paraphrase) it’s worded as Daniel was having a vision in which he saw a separate vision.