It is easier to explain this by describing the entire process than by defining the terms in a vacuum.
Title To Vehicles
There is a law in every state requiring cars on or adjacent to public roads to have a certificate of title in place and to be registered, subject to only very narrow exceptions (e.g. for historic inoperable vehicles).
This is governed by state law. While state law varies somewhat, typically you are considered to have title to a car when a certificate of title is endorsed by the owner and delivered to you as a buyer or transferee. In some circumstances, the term is used in a more strict sense, however, and in a more strict sense someone has title to a car only when the endorsed certificate is submitted to DMV (Department of Motor Vehicles) officials and entered into their database. Being in title to the car means that you legally own it (subject to changes of ownership by operation of law such as due to death or court order, that aren't yet reflected in the official records of the state).
If you own the car free and clear, the owner will be given physical possession of the certificate of title.
Any loans that have the car as collateral must be noted on the certificate of title and made a matter of public record with the DMV. If the car is subject to a loan for which the car is collateral, the lender normally has physical possession of the certificate of title that must be surrendered to the owner when the car loan is paid in full. There is a process for transferring title of a car repossessed for a default on a loan or obligation for which the car is collateral to the purchaser at auction, or the repossessing lender, as appropriate under the circumstances.
If the physical certificate of title is lost or destroyed, a replacement certificate of title may be issued to the registered owner of the vehicle in the DMV database, with the payment of additional fees and additional paperwork or assurances to confirm that the registered owner still owns the vehicle.
Upon initial inclusion of the change in title ownership of the car in the DMV database, the car is "registered" in the DMV database. To register a car, the car owner must provide to the DMV an up to date address (which is binding upon you for service of process by mail of traffic tickets and toll road charges), pay a registration fee and/or car tax, and often, you must provide proof of emissions compliance and/or proof of car insurance in force. An initial registration may also require a physical inspection of the car's vehicle identification number (VIN) by a third-party or government official that is compared to the VIN on the certificate of title, to confirm that they match. Sometimes, a written notice is sent to the previous owner at this time to inform them of the change as a safeguard against forged certificates of title.
Initially registering the car results in the DMV associating a license plate (typically, a new one, although some states permit a license plate to be transferred from one car to another) with a particular car with a particular VIN number. Typically, in addition to the license plate, one is also issued a sticker stating when the car's registration expires that must be attached prominently in the correct place on the license plate.
If the car owner moves to a new state, a process almost identical to the process to change the title of the car to a new owner in the same state must take place in the new state, and the registration and title in the old state are cancelled. Typically, the law requires a new registration and title within 30 days of moving to a new state, but in practice, this requirement is rarely enforced until the old state vehicle registration for the car expires.
Registration typically lasts for one to two years. When the registration expires, one must renew the registration by providing to the DMV the same information and clearing up any outstanding unpaid traffic tickets. In exchange for doing these things to renew the registration on your car, the DMV provides a new license plate sticker with an updated expiration date.
A car owner's car registration must also be updated with the DMV if the owner has a change of address, which is usually done with a simple form and a minimal fee, with new new registration sticker. If this is not done, the owner is still held legally responsible for vehicle related correspondence mailed to the out of date vehicle registration address.
The Consequences Of Failing To Register Your Vehicle
If your car registration is not renewed before it expires, you must pay the car registration fee and/or car tax for the period during which the registration was expired, and often an expired registration penalty as well, in addition to all of the other things that one must do to renew your vehicle registration. When a car changes ownership, the new owner of the car must typically resolve any unpaid registration fees and/or car taxes and other requirements that the previous owner had not kept current, before the change in ownership of the car and initial registration of the car with the new owner is processed.
If you drive a car with an expired registration sticker (from any state) that is past the grace period after the expiration date, the police will routinely stop you.
The police will also issue you a traffic ticket for failing to register your car, unless you can show them that you have registered the car and gotten a new expiration sticker and just haven't gotten around to affixing it to the car's license plate yet.
If the car is parked on a public road or in a driveway connected to a public road with an expired registration sticker, the police will often place a traffic ticket on the car in your absence.
When a traffic ticket is issued (with or without your presence), the ticket will usually specify a fine and a due date and/or court date by which you must pay the fine or show up to contest the ticket in court. If the fine is not paid and you don't show up to court and convince it to vacate the ticket (typically this would be done by showing that your registration is current and the registration sticker fell off or wasn't affixed to the license plate yet at the time the ticket was issued for some good reason, or by demonstrating diplomatic immunity), then the ticket becomes a money judgment against you that the government may collect by means including refusing to renew your vehicle registration until it is paid.
If you have enough unpaid tickets, the government to whom the fines are owed may "boot" your car (immobilizing it) or may tow it and sell it at auction to pay for the unpaid tickets.
Note on terminology: the term "car" in this answer, actually applies to any vehicle that must have a certificate of title and includes trucks, some farm and construction machinery, and some trailers used on public roads.