In the grand scheme of things, a warning letter is a "warning" that the FAA alleges that you have broken an FAR, but is not prosecuting it. A Letter of Correction means that the FAA officially takes the position that FAR(s) were broken and that an agreement has been reached to correct the problem.
If a Letter of Investigation is sent, meaning a file is opened, the FAA Investigator must take some action to close their file. The Letter of Warning is the least the FAA can do. A letter of Correction is used when there is some concern that a problem exists that must be corrected. Mostly these are used to address honest mistakes.
Safety of flight issues and intentional acts are usually addressed by Certificate Action, up to Revocation.
Letters of warning are typically expunged from the FAA's records after 24 months. However, if your employer made a report the incident may be reported under the Pilot Records Improvement Act, which can follow you around for life.
With PRIA, the best thing to do is to disclose everything. Typically a pilot gets hired, is in the middle of training, then the PRIA report from the former employer(s) are recieved and problems start.
Depending on the FAA professional involved, Certificate Action can be started from relatively minor infractions, such as failure to post a revision. One difference between the applicants with 200 hours of sim time and those with thousands of hours of flight time is that the pilots often have something unfortunate to explain. You are not the Lone Ranger. Just make sure you have dealt with the issue in a positive way.
As far as Company Warning letters go - it depends on the circumstances. At our airline we get warning letters for calling in sick when we are physiologically incapable of flying safetly. If given the choice between getting a Company Warning letter and being involved in an incident which could result in a warning from the FSDO, always choose the side of safety and caution.
