It really is very simple.
Everyone has two pairs of grandparents and 4 pairs of great grandparents and 8 pairs of great great grandparents.
First cousins share a pair of grandparents. Second cousins share a pair of great grandparents. Third cousins share a pair of great grandparents.
The 4 people could be a third cousin of, for example, your Mom's 2nd, 5th, 6th and 8th pair of great great grandparents. If that is the case, then they need not be related to each other.
The same can be happening on your paternal aunt's side where the 4 people could be a third cousin of your aunt through her 1st, 2nd, 5th and 7th pairs of great great grandparents. They again need not be related to each other.
These 4 people can be further than 3rd cousins, and if so, they'll have even more of your ancestral lines to differentiate them.
With regards to the additional person related to you, there are two possibilities.
Either she's related on your Dad's side and your Dad happened to get a lot more shared DNA, most of which he passed down to you, than his sister (your aunt) got. Your aunt might have just got under the threshold to be a match, or
You could be related on both your Dad and Mom's side. Both your Dad and Mom passed down shared DNA to you. Neither your Dad (or aunt) or Mom has enough shared to reach the threshold that is considered to be a match. But the combined amount you received was enough and was called a match.