Depending on the format for application that the company one is applying for uses, there are a couple of different ways to go about applying for two positions within the same company, while at the same time maximizing one's chances of getting hired.
The first and most important step when applying for any job is to have a targeted resume. This means that your resume is edited to cater to the position you are applying for. A common mistake that many people make when constructing a resume is to put something like, "To obtain employment with your company," as their job/career objective. Instead, what one should do is write the position applied for and the company in this field. When applying for two positions within the same company, put both positions in this field.
For example (I just got an interview this week with these details):
Career Objective: Front Desk Agent and/or Night Auditor at Middle Beach Lodge
It goes without saying that one should be sure to really target the body of their resume towards the positions they are applying for.
The other option for applying for multiple positions would only be utilized if the positions are located in different departments and/or physical locations, or if there is a different manager for each position. In these cases, one should make two separate applications to each department/locale/manager. Be sure to include a cover letter on both applications.
Again, the key to successful job applications is having a targeted resume. Every job I have ever applied for, I have reviewed and edited my resume to enhance my chances of getting the interview. That's the whole point of a resume, to get you the interview. Once you get to the interview, it's a different story.