Tropes are a great place to begin character development. In certain cases, a trope is enough. In many cases, a trope can become a character.
A stereotype is a trope gone bad.
The difference is subtle but telling. It's all about direction. The stereotype works backwards, grounding characteristics in nothing but the audience's assumptions. A trope--and a character--more forward.
A stereotype says, "Vampires are sophisticated and aloof; therefore, so-and-so is sophisticated and aloof."
A trope says, "So-and-so is a sophisticated and aloof vampire; therefore . . . "
Secret Moon by Siira Gou is a great example of building off tropes. A vampire and werewolf couple may be standard fare; where the book takes off is taking the "given" characteristics to natural, organic conclusions. How does a sophisticated, aloof, and lonely vampire handle a lover whose personality changes in moonlight? How does the lover whose personality keeps changing handle who he has become? What does it mean to the two characters' futures?
Stereotypes are lazy writing--the writer forces behavior for the sake of a plot (understandable; plots are difficult), then relies on stereotypes to excuse "huh, what?" behavior. Um, yes, I know I sent the vampire who doesn't want to be discovered to the school dance but that's um, because, because . . . he is a vampire-in-love!
Less lazy writers may still need to force the plot but they will delve into the trope to piece the characters' behavior together. Skilled writers will find a way to build off the trope, so the characters' behavior (the outcome) appears natural.