All tanks can be divided up into two camps: damage tanks and CC tanks.
Damage tanks build 0-2 damage items and have AoE and/or damage over time abilities that force enemies to focus them before they kill the backline, enabling the carries to do their job or at least allowing the tank to clean up the fight while being the last man standing. Examples of damage tanks include Garen, Shyvana, Dr. Mundo, and Singed. Damage tanks are very strong in solo queue since they require coordination to deal with, but avoid picking them unless you have a champion with reliable engage on your team already (Orianna, Kalista, Annie, etc).
CC tanks have crappy ratios on their abilities (usually) and lack damage in their kit, but have two or more CC abilities and their ult usually allows them to lock down an entire team to start fights. Examples of CC tanks include Amumu, Malphite, Leona, and Nautilus. CC is not optional when building a team comp, making CC tanks a valuable addition to any team comp and a good choice for first picks in draft. The drawback, as you have highlighted already, is that CC tanks require a coordinated ally team.
There are lots of champions who fit somewhere in between, like Darius and Olaf. Most of them are better classified as fighters because of this.