In order to answer this you need to firstly consider that strength is one component of fitness, along with the likes of endurance, speed, flexibility and power. We tend to use fitness as an encompassing term for a person’s physical state.
As a triathlete the majority of time is spent working on aerobic endurance (the ability for your heart and lungs to feed the working muscles with oxygen to sustain activity). Strength is something that is most commonly used in reference to muscular power, which refers to your bodies ability to generate great forces through muscular contractions, for example muscular strength is important to a triathlete when needing to generate force to climb up a hill on your bike or when running. Strength training can be executed either in the gym with weights or it can be done in the real world with hill reps.
In the endurance world base training refers to the period of time that an athlete will spend focusing on improving their lower to moderate intensity efficiency; imagine laying down solid foundations for a project, this is your base period.
This kind of training is most commonly done at the beginning of a long block of training, for example through the winter when starting again after a time of recovery. Base strength in the gym might include exercises doing 2-3 sets of 15-20reps.
Base aerobic fitness includes the long steady easy workouts that are 1hr and longer but done at a steady intensity. The advantages of effective base training is that it creates lower levels of stress and fatigue with less likelihood of injury.