Tiger parenting has been given much attention in the media. That said, in my book The Dolphin Way: A Parent's Guide to Raising Healthy, Happy, and Motivated Kids Without Turning Into a Tiger, I coined the terms dolphin and jellyfish parenting to explore other modes of behavior.
The tiger parent is an authoritarian parent. Some tiger parents are authoritarian "directive" meaning pushing and directing their children. Other tiger parents are authoritarian "protective" meaning hovering and micromanaging their children. Either way, tiger parents usurp their child's sense of internal control and self-motivation.
The jellyfish parent is a permissive parent. They have few rules or expectations, and often overindulge their children. Children of jellyfish parents tend to lack impulse control.
The dolphin parent is the balance of these two extremes and is authoritative in nature. Like the body of the dolphin, these parents are firm yet flexible. Dolphin parents have rules and expectations but also value creativity and independence. They are collaborative and use guiding and role modeling to raise their kids.
Here is a chart outlining the differences in these styles: