What is a carrier?
Carrier is a commonly used term in the US and Canada for a company that provides voice or data services. These services can be either wireless or through wired landlines. (For example: T-Mobile, Verizon,Sprint, Time Warner, AT&T, Cricket Wireless, etc.)

What is a no-contract phone?
When a cellphone is bought, the customer will have an option to either buy the phone with a subsidized price and sign-up with the said carrier or pay-up the entire cost of the phone and choose a carrier of his/her choice. While the former comes with typically a two year contract which binds the customer to stay with the carrier for the said period and requires a hefty termination fees to be paid in case he chooses to switch to another carrier within the contract period, the latter is called a no-contract phone. Almost all phones and carriers in the US have both contract and no-contract plans.

How to own cheap cellphones without contract?
No-contract phones can be bought with two types of payment options. One is to buy a lump sum amount as a one-time payment and the other one is through installments payed through PayPal or credit cards with an interest fee distributed over the period of payment. If the usage of the phone is limited to just text and call, it is better to pay for the phone upfront and have a flexibility to switch over carriers whenever preferred based on the type of plans offered.
At the same time, prepaid, also known as pay-as-you-go options, are offered by most carriers these days which means you can buy a phone of your choice with an amount paid in advance for the services to be used. This will help to control the budget on phone usage itself and also not paying unnecessarily for the features that are not used. Once the prepaid amount is used up, the phone can be returned back or topped-up (prepay the amount again) to continue with the services.

Prepaid phones eliminates the costs incurred on activation, overage, changing carriers, and termination fees, and at the same time gives the flexibility to choose the phone and the carrier making it a cheaper option over the traditional contract phones.
Although no-contract plans are offered by all major phone manufacturers, only some phones will be compatible with the carrier’s network. So, this has to be kept in mind while buying a phone or a carrier to save up on unnecessary charges for the features that will not be usable.
It is also a cheaper option to own a basic model if the usage is limited to just voice and texts. As there will be no features in the phone to get updated, the overall life of the phone itself will increase. Retaining the phone for more years helps in recovering the initial investment on the phone.