But as gardeners, we use terms in different ways: We talk about "grass types" to refer to different kinds of grass in a seed mix (normal seed mixes), e.g. festuca or lolium varieties. And we talk about "lawn types" to refer to decorative, utility, sports or other landscape lawns - because they have different functions. For example, a decorative lawn is not as resistant to stress in a domestic garden as a utility lawn, which is better suited to children's games (often referred to as a "games lawn").
However, this type of lawn would not be suitable for a football stadium because the grass there is under much higher stress. Football fields require proper sports lawns. The seed mix defines the lawn type in greater detail. After all, there is the right seed mix for each type of lawn. Make sure what your needs are, get advise in the garden centre and choose the right mixture.