Lots of questions, lots of answers.
In the professional theatre there are a large amount of different levels. These levels are determined by the location of the producing company, it's budget, and the size of the venues. At these levels the companies produce ORIGINAL work. A tour is not original work, it is a COPY of an original. In descending order of prestige it goes:
Broadway - Only in NYC, also classified as LORT ((http://www.lort.org/)
Off-Broadway - Only in NYC, generally LORT A or B, Obie-Eligible
Regional Theatre - Anywhere in the country, LORT B, C, D, Eligible for local awards and the " Best Regional Theatre" Tony
Off-Off Broadway - Non-LORT NYC companies. Very small budget. Essentially, the fringe scene but with added cred for being in the city.
Local Fringe Professional - Non-LORT, Non-NYC companies that still pay everyone.
Semi-Professional - This is where they stop paying everyone, but still pay some people.
Community - This is where pay disappears, except for maybe the director
Academic - High Schools, Colleges, etc.
Tours. When someone produces a show on Broadway and it becomes very popular, they will decide to take that show on the road. They will create a touring company that is a completely new cast, but utilizes IDENTICAL staging, sets, lights, choreography, etc. as the original Broadway show. If you are seeing a Broadway tour, you are seeing an exact COPY of the Broadway production.
That tour can travel nationally or regionally. If the producer of the tour decides to restage the play or tour a copy of a production that was not ever on Broadway (even if that play was on Broadway) it is generally considered to be a National Tour or Regional Tour.
So, if I did RENT on Broadway and then duplicated THAT production and performed it in Chicago, that would be a Broadway Tour. If I did RENT in Texas at the Alley Theatre (LORT B), and then took it to Cleveland that would be a National Tour. If I did RENT in Boston at the Merrimack Repertory Theatre (LORT D) and then took it to Providence and had no plans to leave New England, it would be a Regional Tour.
With me so far?
Auditions for Broadway and National Tours. Almost all of these will be held in NYC. Backstage Magazine and Playbill.com ((http://www.playbill.com/jobs/find/)
are great resources for finding auditions. HOWEVER, all Broadway, National Tours, Regional Theatre, and most major professional theatres employ almost exclusively EQUITY ACTORS. An Equity Actor is someone who is in Actor's Equity, The Actor's Union. (Please see their website for information on joining. It's a very long and complicated process. They only accept people who have proven their professionalism though achieving points. http://www.actorsequity.org/)
Occasionally, big shows will hire NON-EQUITY chorus. If you want to be in one of these big time should you will be looking for NON-EQUITY CHORUS CALLS. You may also see OPEN CALL. That means that union and non-union actors will be auditioning together.
If you don't live in NYC, you're limited to your local Regional Theatres. Many smaller theatres will have Non-Equity auditions as well. Find out what companies produce in your area and check out their websites. Remember, not all venues are producers. If you have a favorite theatre where you have caught the National Tours of all the Broadway hits, it is likely that this is not a producing venue. They do not hold auditions, only book in complete productions for short stints. Theatres on the LORT list, ARE producers and make their own work.