I was told that OSHA's rules are federal standards and as so, apply to every business in America. Is this true?

There are different rules for different types of companies. There are some that apply to all...for example:

If Jane falls and breaks her arm at work...it doesn't matter if she works in a two person office or a large manufacturing company-the incident still needs to go in a log. But you probably won't find an MSDS book in the office as opposed to the manufacturing company.