If it doesn't fit under the seat in front of you then it is a carry-on. If it DOES fit under the seat in front of you then it is a personal item. You cannot bring a carry-on if you have a Blue Basic fare; you'd need to either check it at the counter ($30-35) or at the gate ($65).

Several airlines do not include carry-ons on the cheapest fares - JetBlue, United, and probably most of the ultra-low-cost carriers like Spirit and Frontier. American and Delta do not have this type of restriction.