The basal/bolus terminology serves as a way to conceptualize and facilitate insulin dose calculation. The terminology is useful in that regard. More advanced pumping techniques like extended boluses to cover a certain nutrient profile utilize the basal/bolus terminology because that’s how the pump hardware designers configured the pump. The distinction between basal and bolus is important simply as a way to communicate a dosing technique.
Basal and bolus meaning can be blurred with how they are deployed. Basal insulin in a pump can be used in a bolus fashion. One example I read today was someone who had a 30 minute basal period starting at 3:00 a.m. with a basal rate that delivered 1.5 units in that half hour to neutralize a strong dawn phenomena.
Or a bolus can be extended for many hours to match an extended fat/protein digestion process and look more like a basal delivery.
People on MDI also call the long-acting insulin as basal insulin and the short acting insulin as bolus or meal insulin.
I agree that the black and white definitions of pump basal and bolus are not, in practice, neatly and clearly defined. Instead, like many things, there’s a spectrum of function that overlaps both of these terms,