As I answered to my own question.
You'll have to explain what you mean by overlap (how?) and connect (in what manner?)
Then I await an explanation.
The study of early life is still the study of biological evolution. How it came to be comes down to determining what early life was like and where it came from. The very very beginings of abiogensis mostly deal with thermodynamics and chemistry. Once we get to early forms of rudamentary processes that resemble heredity we get into a more grey area of whati s biology and what is no biology. Self replicating protiens that gradually become more and more advanced to the point of developing lipid bilayes to become more distinct as well as the development of what can be describe as a simpler form of RNA appears and again I ask if you still don't see the connection between the study of evolutino and abiogensis. In fact it usess evolution as a basis for the theory. Without evolution there is no abiogensis. Nothing in the theory makes any sense without evolution.
Just to recap.
1. Evolutionary processes did not start with life. IT started prior to life during the grey period. To suggest otherwise suggests special creation which is unscientific.
2. The basis for abiolgenisis is nearly 100% rooted in evolution with helping hands from other branches of science such as thermodynamics and geology.
3. It is the study of the beginigng of evolution. Abiogensis, especially when talking about the tail end of it just before it becomes life as well as having the conversation of where we draw that line (much harder than one would think and is still debated today)
4. You will not quote me saying that abiogensis and evolution do not have their differences. The study of life a million years ago and how it changed is fundamentally different than how we study the origin of life. But you cannot say they are not connected. You cannot say they have nothing to do with each other.
Whatever it may be: an act of god (special creation), panspermia, or abiogenesis.
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Do you know what that means when you list these three?
Special creation (god) is not considered in science. IF we have evidence of it great it will no longer be special creation but just creation with measurable and defensible points. But this is already thrown out of the window when talking in the context of a science. Even if you believe in theistic evolution where god's guiding hand used natural processes to bring about evolution you still have no need to believe in special creation as you could then simply believe that the creation of life is as abiogenisis suggests and that it was simply god's will via natural processes.
Panspermia is not really supported by any evidence. Its "possible" through big leaps. Typically any seroius conversation is dfiscussing Mars having developed early forms of life and it was some how jetted over here through a massive collision of some kind at just the right time for Earth to accept life. This seems far less likely than it simply developing on Earth. It also kicks the can down the road. If it wasn't abiogensis here then it was abiogensis there. Still back to abiogensis but simply adding unecessary steps.
Lastly you have abiogensis. The only real explanation one has when talking evolution with any degree of scientific or empirical judgement. Any other discussion is really non-scientific with the only exception being "the unknown". Saying we don't know for sure is a correct answer but it is also a misleading one. We do have a "best scientific explanation" for the phenomenon. Unless there is a god who has neglected to show himself in any other way shape or form except to start life, life must have started on its own. That is a fact.