No, as the pictures show they are absolutely not even remotely the same thing
A turtle freeze might be a progression to a peacock pose - which is much closer to a full planche, but is much easier than a peacock or planche. The main differences come down to an altered center of gravity and how this impacts the effort required to balance the body on the hands:
Leverage - In both a planche and a peacock pose the body remains straight. This increases intraabdominal stress by resisting torque provided by the extended body. In the turtle freeze, the extremities of the body are pulled much closer to the center of gravity. This reduces the effort required to hold the body in position.
Larger base of gravity - In both the planche and peacock pose the hands are kept symmetric across the midline of the body, which provides a very small base for the center of gravity to rest in to maintain balance. However, the turtle freeze has the hands in asymetric positions giving a much larger base, and thus greater margin for error. Unlike in the plance or peacock where the position must be very static to hold, this allows for greater opportunities to shift weight in the turtle freeze.
Freeform vs strict form - The planche (and I'll assume peacock pose because of the similarities) are strict movements, which must meet a number of criteria to be considered "correct", among these are the symmetry of the move which requires the body to act in unison and have uniform strength bilaterally. This is in contrast to the turtle freeze, which is an exhibition activity and takes advantage of the freeform rules - this allows a breakdancer to take advantage of unilateral strengths (which are usually present due to the phenomena of 'handedness'). Similarly, a turtle freeze has greater room for interpretation as long as it suits the performance.