Your guess is correct. The signature is very different. In order to reach LIGO's frequency band, the objects must be very compact. If they are too large, they

Your guess is correct. The signature is very different. In order to reach LIGO's frequency band, the objects must be very compact. If they are too large, they touch before they can orbit each other at sufficiently-high (audio!) frequencies. The Schwarzschild radius of the black holes in question are less than 100km in size, while the size of a star as small as our Sun is ~700,000 km in size. Moreover, the compact objects (neutron stars, black holes) that LIGO can observe are exceptionally dense ( > 3x10^17 kg/m^3), while stars have roughly the density of water (1000 kg/m^3) on average, and much less at their extremities. Compact objects can disrupt nearby stars long before they could touch, spreading the "merger" across many, many years (many, many millenia, I suspect), rather than the fraction-of-a-second typical of a LIGO black-hole observation. For a visual image of the interaction of a large/fluffy star with a compact object, have a gander at a few of these images: https://www.google.com/search?q=roche+lobe+accretion https://www.google.com/search?q=roche+lobe+accretion