Are all groundcovers considered invasive?
Not at all, in fact most are not. The whole point of a groundcover is to spread and cover some real estate and many consider this to be "invasiveness". It is not. The only valid definition of a groundcover is that of a low growing, spreading plant that covers the soil in its growth habit. That fits a huge range of plants, many of which are not considered true groundcovers in the traditional sense and have no invasive or even aggressively spreading tendecies at all. BTW, "invasive" is generally used to refer to exotic (ie., non-native) plants that easily escape cultivation and colonize natural areas to the detriment of native species. English ivy and in some cases, vinca, are considered invasive as they often escape from gardens and become problematic.