Motility is a biological term: the ability of an organism or cell to move itself, using its own energy — sperm motility, bacterial motility, gut motility. Mobility is the general word for the ability to move or be moved, and applies to people, vehicles, capital and furniture. Motility is always self-powered; mobility need not be.
The core difference
Both concern movement, but motility is narrow and technical.
- motility — self-generated movement, chiefly biological: sperm motility, intestinal motility.
- mobility — the general ability to move or be moved: reduced mobility, social mobility.
Where each appears
Motility belongs to biology and medicine almost exclusively — you will meet it in fertility testing, microbiology and gastroenterology. Mobility ranges far wider, including figurative uses like social mobility, which describes movement between economic positions rather than physical movement at all.
The roots
Both come from Latin movere, to move. Motility was coined much later and deliberately narrowed to self-propulsion, which is why it kept a precision mobility never had.