Condensation around stars leads to a predictable mineralogy based on the composition of the atmosphere of the star. The condensates, like stars, may be oxygen-rich or carbon-rich. The first presolar grains discovered were all C-rich. Minerals such as diamond, silicon carbide and graphite are resistant to acid processing and so most of the meteorite could be removed by acid dissolution leaving a residue of the carbonaceous grains.
The characteristic used to distinguish extrasolar grains from solar is the presence of isotopic anomalies. Silicon carbide has carbon isotopic compositions that range over three orders of magnitude! Such variations are present because of stellar nucleosynthesis that creates and destroys individual nulides. Moreover, the solar composition is an average of many components so any extraterrestrial composition that is an average of different components will be anomalous as well.
The isotopic structures present in presolar grains allow us to see origins in red giants, supernovae, novae and possibly Wolf Rayet stars. This is no coincidence, these stars are characterised by high mass loss, rapidly dumping enormous amounts of dust into the interstellar medium. There they are swept up into molecular clouds before being incorporated into new stellar systems.