It sounds also that there is a difference in when they can see:
Truesight needs line of sight (LOS), but not line of effect (LOE).
Blinsight needs LOE but not LOS.
Which in odd situations can cause a difference - for example, blindsight could see the assassin behind the tend (blocks LOS but not LOE), but not behind the transparent forcefield (blocks LOE but not LOS)... and vice versa for true sight.
Now, if the creature with blindsight also had regular vision, it could use its regular vision to spot the guy behind the force field... that said, a LOT of creatures with blindsight are, well, blind.