Q:

Same Department Hires Two Positions But How Should I Apply?

The situation is this:

The same department and the same hiring committee has posted Position A which will close soon and Position B may be posted later (but do not know when)
Position A is a contract position that ends in March next year; Not sure at all if it will be turned into a long-term continuing position.
Position B is a 1-year position; Potentially turns into a long-term continuing position afterward. (This position sounds more promising)
Learned about Position B through a worker from the department but the worker is not part of the hiring committee.
I have the qualifications and experience for both Position A and Position B, but perhaps better suited for Position B.
I am currently not working at that company but wish to work there for long-term.

Now here are my concerns:

Position B is more promising and better suited for but I am not sure when it will be posted. Should I still apply for Position A and just to get my foot in the door first? In other words, apply to both?
If I do land an interview for Position A, should I mention about Position B?
How should I go about expressing that I am more interested in Position B than Position A?

A:

Position B is more promising and better suited for but I am not sure
  when it will be posted. Should I still apply for Position A and just
  to get my foot in the door first? In other words, apply to both?

Yes, apply for both. You don't know how many applicants each position will receive, i.e. what your chances will be for either. 
So the best strategy to maximize the probability of being hired for either is to apply for both as soon as you can, once you prepare your application materials. 
Note: Make sure to tailor your cv and/or cover letter appropriately to the requirements of each role.
In general, by not applying, you are also deciding not to be hired. It's your job as the applicant to apply for jobs; it is NOT your job to decide whether to hire you -- so leave these decisions to others, and don't worry about it. 
If this feels/seems "weird", etc. -- same point applies. Just go for it, and let HR and the hiring manager decide if it's weird, odd, etc. -- your task is to secure a foothold in the organization, and applying for ALL positions for which you feel qualified is the surest way to achieve this goal. 

If I do land an interview for Position A, should I mention about
  Position B?

No, wait for them to mention it, and if they do not, this means it is not relevant to the interview at hand. Focus on answering the interview questions, and not answering questions you are not asked -- and you will do that much better. 
If you end up getting both offers, that's what you want -- to be in a position to choose what's best for you. Politely decline one and accept the other. It is business, and it is absolutely acceptable for an applicant to pursue multiple opportunities, whether with the same department, same company, or different employers. 

How should I go about expressing that I am more interested in Position
  B than Position A?

You don't express that you are more interested in either position. Customize your application to each position, and put your best foot forward. It is not up to you to decide what you are better suited for, but the hiring manager's. 
Keep in mind, position descriptions often differ from what's in the hiring manager's head. The job they have in mind might not be accurately reflected on paper, and only the manager will know whether you seem a better fit for this or that role. 
Let them make that decision, and concentrate on presenting yourself as the best candidate for each position for which you apply. Good luck!

