Are the IMU velocities equivalent to the GPS ground velocity, except for the coordinate reference system?
An IMU uses gyro and accelerometer measurements to calculate its velocity vector relative to the Earth.   Similarly, a GPS uses range, range-rate, doppler, and/or carrier phase shift measurements to several satellites to calculate the same velocity vector.  So, an IMU and a GPS calculate the same velocity vector, but use different measurements.  

The difference between the IMU and GPS measurements are that, inherently, an IMU has very good short-term accuracy but drifts over longer periods of time;  a GPS has very good long-term accuracy, but is very noisy over short periods of time. Therefore, IMU and GPS measurements are usually combined to provide a navigation solution that is accurate over both the short-term and the long-term. 

The components of the velocity vector are usually given in a local-level, local-north reference frame; for example, the north- east, and down components: $v_N$, $v_E$, $v_D$. The ground speed is $v_H=\sqrt{v^2_N+v^2_E}$.