I use these terms interchangeably, mostly out of convenience. But I have a fairly large inner battle about it every time. I feel that "teenager" is closer to slang and "adolescent" is closer to an academic term. I tend to use "adolescent" when I am writing for an academic setting, and "teenager" when I am trying to reach a wider audience. I am not sure that it matters.
I am always concerned with conveying respect for this age group in general and that is done in more relational ways like always recognizing their value, giving them equal weight in their opinions and ideas, and in never underestimating or assuming the worst about either the group or an individual student. It can also be done in writing. I think that all of these terms, like many terms, can convey either respect or disrespect depending on the context. Teenager is the term, I think, with the most potential for disrespect because it is the term most frequently used in pop culture and usually brings to mind the stereotype, and not an individual or even the age group. It makes sense, then, to steer away from using it. However, because of its popularity it often reaches the widest audience. Adolescent is the word that does bring to mind the age group, the developmental stage and a good deal of the research that is available. It is the term that is used the most frequently in academics, and, I think, the word that conveys the most respect for the population.
I also find myself using terms like student, young adult, emerging adult, and youth... the lines get blurry. But, in the end, it sometimes boils down to variety for my readers and myself. Because I am so passionate about this age group, this stage of life, I have to use more than one term just to stay sane. I tend to use adolescent in academic writings, and teenager in writings that interact with pop culture or stereotypes, and young adult or emerging adult when I am talking about someone who is of age to have graduated from high school. But these are just rules of thumb. In end I have to say something just to write, so bear with me as I figure it out.