How does philosophy define life? And how does it overlap and contrast with the concepts and nuances of other sciences such as biology, chemistry, physics and mathematics?
They ask different questions. Philosophy may ask what is life, is there a purpose behind it, etc. Biology asks how does it work, chemistry what are the chemical reactions that drive it, physics maybe how does physics allow for life and how life utilizes and impacts physics, and mathematics how can life and its components be described mathematically.
It is good to remember that all scientific disciplines branched off from philosophy (and religious philosophy) and that they are interconnected.
This is the answer to the part of your question that includes biology. If you want to discuss the meaning of life philosophically, you are welcome to come to do it on the philosophy page!
There is no difference along the lines of philosophy vs. science. However, there are broader and narrower definitions in biology.
The broadest I know of is "a self-replicating, chemical system (thing) with both exhibits heredity and some form of homeostasis (display internal negative entropy)", and some even argue the last part may be optional.
The narrowest also requires being made of cells, displaying growth, metabolism, adaptation, and response to stimuli. Some argue against these because they are either implicit in the other definition (homeostasis requires a metabolism, self-replication + heredity = adaptation), that they are unnecessary (cells or growth) or difficult to define themselves (response to stimuli).