Mowing, fertilization, mulching, trees, shrubs, flower beds etc. are considered softscape. Basically everything to do with living things. Hardscape refers to wall, patios, walks etc. Basically all the "hard" things. In my neck of the woods it's all considered landscaping, since the landscape includes both soft (living) and hard (non-living) things and everything you need to install and maintain them.
Lawn care involves some routine seasonal tasks like trimming and edge, weed removal and fertilizing, mowing and watering, etc., On the other hand, Landscaping is the act of transforming an outdoor area by plantation, construction, or reorganization.