Type A personalities are generally thought of as high-energy, high-strung, high-risk for heart attacks. Everything must be perfect, on time (preferably early), and in order. They are goal-driven people who are often told they need to "slow down." Failure is essentially forbidden to these types--they work extremely hard and are highly competitive. They like to succeed, but more than that, many often claim a need to succeed. They function under extremely high stress rates, but this can be detrimental to the health of a Type A.
Type Bs, on the other hand, are more relaxed. They work toward deadlines but do not stress over them, and if they are achieved, this is acceptable. If they are not, Type Bs typically do not become overwrought. They are also nowhere near as competitive as Type As, often simply enjoying the activity or just not participating. Usually Type Bs take more time to reflect on things, whereas Type As are more likely to take immediate action.