Exact requirements for SR50s and SR16s differ according to state laws. These specific forms are most commonly used in Indiana when IN motorists involved in accidents or who have received citations for traffic offenses are required to submit one or more forms to the BMV.
In Indiana the SR-16 is a form used by courts to notify the BMV that a driver has been convicted of, failed to appear for, or failed to pay a citation for violating a motor vehicle law. This form also notifies the BMV if any of the above orders have been rescinded.
So if you are getting your license reinstated by the court then the clerk of the court's office will produce a SR-16. This form will allow the BMV to clear your license. Normally the Clerk's office will mail the form to the BMV however some allow you to hand-carry the SR16 to the BMV, to expedite the reinstatement of your license, for an additional fee. If this option is available at your Clerk's office then they will produce the form while you wait so you can take it to the BMV special reinstatement centers. So to find out about this form in Indiana, contact the clerk of the court's office.
A form that you did not mention but that some states require as part of the license reinstatement process is the SR22. The SR22 form is used for proof of financial responsibility by drivers who have been convicted of an offense which requires the driver to maintain financial responsibility for a three-year period. An SR22 must be filed with the BMV for three years from a date determined by the BMV. If you need a SR22 then you will need to obtain the required insurance coverages that the state is mandating you carry and then have your insurer file this form with the state for you.
The SR-50 in Indiana is a form is used by a motorist to provide proof of current insurance to the BMV. The form shows the BMV the beginning and ending dates of the current policy. For example the IN BMV notes that if a person is not insured at the time of a violation, they may be subject to a one year suspension of their driving privileges, owe a reinstatement fee of between $150 to $300 and will be required to have an Affidavit of Current Insurance, or SR-50 form, filled out and returned to the BMV by their insurance company.
The Indiana government site has the Affidavit of Current Insurance "SR-50" form online if you wish to look it over.
So these forms are not types of insurance but are forms showing the department of motor vehicles certain things. If you are required to obtain certain insurance coverages to reinstate your driver's license then the court involved or the DMV should be able to inform you exactly which auto insurance coverages these are. You then can inform your insurance agent who can then help you obtain these coverages and fill out the SR-50 form and if the SR-22 is necessary file it for you as well.