Learn English – Difference between “been to” and “been in”

A in that sense is a preposition meaning the same thing as per. Any dictionary will have that as a definition for a (Dictionary.com):

preposition
each; every; per: ten cents a sheet; three times a day.

Oxford Dictionary Online and Merriam-Webster have similar entries.

So there is no difference in meaning between your examples. As to usage differences, per is characterized as being more formal and careful, so you would see it more in academic or legal writing or precise instructions, while a would be more common in speech and normal writing.

The three prepositions imply three different things:

For emphasizes the employer-employee relationship. If I work for a company, they issue my paycheck, and they can fire me for poor performance.

At emphasizes the locale where I work. If I work at a company, I usually park in their parking lot, and work in their building each workday.

With emphasizes that I'm part of a team. If I work with a company, then that company's workers are my co-workers.

The words are essentially interchangeable in many contexts, because many of us do all three at the three time. If I was employed at Nike, for example, I could say that I work for Nike (they issue my paycheck), at Nike (I work in their building), and with Nike (I work with their employees). Quite often, saying one implies the other two.

One of the three prepositions may become less appropriate if one of those three conditions isn't true. If Nike hires me as an independent consultant or specialist, and they allow to me work from home, I might be less prone to use at. If I serve on an advisory board in a part-time, volunteer capacity, I might be more inclined to use with, and less inclined to use for.