Ron Mattocks, a former real-estate sales executive and Army captain, is a Type A personality. He is ambitious, drives himself to achieve and usually succeeds.

One job that really tests his limits, though, is raising two laid-back Type B kids.

When his stepdaughter Avery, 8 years old, or his son Sawyer, 7, start to daydream and wander away from a chore, Mr. Mattocks occasionally erupts. 'The first thing out of my mouth is, 'What the hell are you doing?' ' he says.

When parents and children are temperamental opposites, the results can be explosive. Type A parents, driven by nature, often have to ease up on Type B kids, who are more dreamy and mellow. When the pattern is reversed, relaxed Type B parents often feel outpaced by revved-up Type A offspring. These matchups can cause conflict beyond the normal parenting challenges, and solutions may require parents to adjust expectations and tactics.

With more competition for college admission and a shift to more-involved parenting, Type A parents seem especially evident. The Type A and Type B labels were created decades ago by cardiologists studying the effects of a chronically driven, time-pressured personality on heart-attack risk. Researchers found no link, but the labels remained in use as shorthand for broad differences in temperament that are largely inborn.

Mr. Mattocks, a social-media marketing consultant, says three of his five children are Type A, meaning they usually strive to achieve goals and respond to consequences. Avery and Sawyer are more creative and less motivated by short-term results. When he tells Avery to clean her room, 'she could be up there for hours