I have to agree that an AM for an agency and a sales position have similarities, but as you noted, very different compensation structures and day-to-day experiences. Take the plunge and see what you think, there really isn't any other way to compare without experiencing it first-hand. Truly the worst that can happen with ANY job is that you learn more about what you like and dislike, and meet new people. You then use that knowledge to make decisions regarding the next step in your career. We are all free to change our mind, restart and reinvent who we want to be.
If they believe you are a fit, and you still want the job, go for it. The reality is that any experience you have always gets remixed with each company you join because of new processes, culture, way of communication etc. There is always a learning curve when starting a new job - even for seasoned pros.
Is there a particular area in your studies that you like? Another way to think about it is to find a product or a company you admire or would like to work at and see what marketing positions are available. Pretty much all the categories you mentioned are great for entry-level if the job description's qualifications say so.
Sometimes you just have to get your feet wet to know what you want to specialize in so listing out your dream companies or preferred industries may be a way to start narrowing things down. This gives you an advantage in the interview process because you can talk about your personal passions and how they all connect to the company/product.
A big DO: highlight skills and accomplishments specific to the job description.
Yes, this means you should be tailoring your resume for the position - not a one size fits all. Even if the title is the same, every company is different and there will always be differences in the job description you can focus on to stand out.