A "starter" usually refers to sourdough, or wild, yeast strains—whether captured from the air, or grapes, or handed down for hundreds of years from Italian bakeries. Starter cultures almost always include yeast and bacteria cultures that live and work together in a symbotic relationship (most sourdough starter taste actually comes from the bacteria and not the yeast).
A poolish (or biga) usually refers to a mixture made up with commericial yeast—IDY,ADY or CY—all varations of Saccharomyces cerevisiae, and includes no bacteria right out of the packaging. A poolish (or biga) is a method to extract more flavor (and other effects such as texture) from Saccharomyces cerevisiae, which while ultra reliable and hearty in terms of rising doughs with gas production, has very little flavor of it's own since it has no bacteria out of the bottle to have a symbotic relationship with. Perhaps the added fermentation time involved with a poolish or biga involves some bacterial action, or maybe it's just the acid accumulation from the yeast, I am not really sure. However the added fermentation really does elevate Saccharomyces cerevisiae fermented doughs to a higher level on many levels, including taste.