Ins13 is a 13 variable EKF (enhanced kalman filter). For instance 6 of the variables are 3D position plus 3D rotation.
Ins14 is a 14 variable EKF, it adds automatic trimming for a sensor, I forget which, maybe yaw gyro.
EKFs converge to an answer that in some sense is the best mathematical guess at the state (i.e. where the quad is and where it is pointed) given the current (noisy) sensor readings and a simplified (linear) model of how the system works.
Basic (the complementary filter) is a simpler way of calculating some of the state, and can be done on a slower CPU, but it can be fooled, for instance if you fly a continuous banked coordinated circle, it eventually thinks it is level when it is actually banked. This and other similar issues make it unsuited for autonomous flight.