A bioship, or living ship, is a spaceship made organically using biotechnology. It lives and grows and heals in space, therefore making it formidable in space battles. Over time they can evolve into a species, or may have originated from a species that became spacefaring and took to the stars organically.
It can have different levels of sapience, from being non-intelligent plants, to having animal-like instincts, or being completely intelligent and self aware. If sapient, they range from being cyborgs to full organic technology.
Bioships can use advanced biotech to grow internal drive systems and to collect fuel or other energy rich material like antimatter or exotic matter. Using the same tech, they could replace soft fleshy shells with tougher chitinous layers or even steel or high density carbon constructs, thus making use of all technology within one living, 'breathing' construct.
They can originate from being a travelling Dyson Tree, or some species of bioship are capable of reproducing entirely from seed or by viviparous birth, and can breed independently making them breed out of control and become potentially dangerous.
Moya is a bioship from Farscape.