In what way does Blindsight compliment Truesight?

While the definitions are quite clear,

Blindsight being:

A monster with blindsight can perceive its surroundings without relying on sight, within a specific radius.

Creatures without eyes, such as grimlocks and gray oozes, typically have this special sense, as do creatures with echolocation or heightened senses, such as bats and true dragons.

If a monster is naturally blind, it has a parenthetical note to this effect, indicating that the radius of its blindsight defines the maximum range of its perception.

and Truesight being:

A monster with truesight can, out to a specific range, see in normal and magical darkness, see invisible creatures and objects, automatically detect visual illusions and succeed on saving throws against them, and perceive the original form of a shapechanger or a creature that is transformed by magic. Furthermore, the monster can see into the Ethereal Plane within the same range.

it’s easy to see that they each have their own unique applications. However, there seems to be a range of overlapping between these senses when it comes to visual illusions that brings up many questions, mostly formated as:

Does Blindsight allow a creature to ____________ like Truesight does?

Eg.:

  • Does Blindsight allow a creature to see in normal and magical darkness?
  • Does Blindsight allow a creature to see invisible creatures and objects?
  • Does Blindsight allow a creature to automatically detect visual illusions and succeed of saving throws against them?

I apologize if this is a duplicate question, as I am sure it’s been asked before, but as I didn’t find it in the search, I thought it would be interesting to see the comparison between these two types of senses, focusing on what’s similar between them.