No, that is not normal. It is totally dishonest.
In the U.S., anyway, "fired" is normally understood to mean that the company terminated the employment relationship because of misconduct on your part. I guess that could range from the truly serious, like beat up the boss or stole thousands of dollars worth of company property, down to minor issues like being late for work.
If you make the decision to leave, that's called "resigning", not being "fired".
In the middle is "layed off", where the company lets you go, but not because of misconduct, usually because business has been bad and they have to reduce the number of employees.
As others have noted, these days fear of lawsuits often makes companies unwilling to say the circumstances of your leaving, but simply to say the dates that you worked there, period. I haven't seen a letter of recommendation in many years.
The difference is also important for unemployment benefits: In most states, I think, you can receive unemployment benefits if you were laid off, but not if you resigned or were fired.