The life that we have available to study on earth right now has a common ancestor. There may have been multiple abiogenesis events, but life on earth stemming from other abiogenesis events has either died out, merged so as to be functionally indistinguishable, or has not been discovered. I am unaware of anyone working in biology under other models.
I suspect, as you do, that any Martian life will likely be recognizable as "life". The long term fear is of course that either things from earth will eat all of it, or it will eat everything from earth (that's less of a concern since quarantine in that direction is pretty easy). The short term is what we really need to be concerned about though. In the short term, the concern is that Martian life will be mistaken or written off as life from Earth.
This problem is exacerbated when we consider that the life on Mars that we are looking for could be former Earth life that hitched a ride on some rocks millions or billions of years ago. If we scoop up some Martian soil and find a few rather prokaryote-ish looking things bopping around in it, then exactly what we have just found becomes very hard to determine if our spacecraft was not sterile. Did it just find an example of convergent abiogenesis and evolution? Evidence of panspermia? Or did somebody in the assembly building sneeze on the scoop?