A pest is defined as an animal or plant that is considered a nuisance to humans or damaging to human structures like houses. Let's take the first two examples, a grouse and a squirrel. Grouses are a type of large bird, about the size of a chicken. They are generally not considered pests as they do not damage structures and eat mostly insects. I suppose if they took up residence in your yard eating on your plants and shrubbery then you could consider them a pest. Squirrels, on the other hand, can be pests to your home. They do not eat or destroy wood, but if they get on your roof they can make their way into your attic or behind your walls from under the eaves. They like to nest there, especially in cold weather.
Grass and dandelions are different in that they are both plants. They do not actually damage humans or buildings, but they can serve as an aesthetic nuisance to people in their yards. Dandelions are technically weeds and most people don't want them taking over their grass. Grass is what most people want covering most of their yard, but for certain areas like plant beds grass would not be desired.