the difference between the paying of the usual Fee for extending Your Visitor Visa and a few Pesos less of s Fine when leaving the country without extending the Visa during the stay is simple:
Who extends His/her Visa on Time is a Legal Visitor with a Legal Immigrations staus during the Time of His/her stay in the Dr, allowed to drive a Car, all Medical Insurances etc are Valid, while the Visitor who just let His/her Visa expire and waits to pay the simple Fine upon Departure is living here on a Illegal Immigrations Status, NOT covered by any Insurance(NO foreign Nor Local Medic Insurance applies for a Traveller with an Illegal Immigrations Status, at all countries around the globe, so if you do not plan to keep your papers in order to save a few bucks, no need to bother to pay anything for any medic insurance or car insurance etc etc, as they anuways would not be Valid anything) and of course Your foreign drivers license will not be valid neither, along with many other thingies travellers bring/pay for, b'c they always in the fine print depend on Your Immigrations Status, in Any Country of the Globe.
a simple and often actual example:
You rent a Car,
You have a Intl/whatso ever Drivers License,
You pay for Full Coverage Insurance(with CC or cash right here),
Your Visitor Visa expired by 1 simple Minute,
You have NO INSURANCE due NO VALID Drivers Licence due NO Legal Immigrations status.
and other even more common simple example by experience:
Your Visa expired by 1 Minute,
You have a great and fully covering Travel Insurance,
You have an accident or Health prob a minute after Your Visa Expired,
YOU are a Illegal Allien by Immigrations Status,
Your Insurance will deny Your coverage, any Coverage,
due that NO Hospital in this Country will accept You for any kinda treatment.
aside of such unimportand lil thingies,
stay and pay your fine at the airport when you leave the country,
and all is just fine
Happy Travels
Mike