No, time dilation due to velocity is not an illusion or a recording mistake. It is a real and well-established phenomenon in physics, predicted by Albert Einstein's theory of relativity. Both time dilation due to velocity and time dilation due to gravity/acceleration are valid and have been confirmed by various experiments and observations.
According to the theory of relativity, time dilation occurs when an object or observer is moving relative to another object or observer. As an object's velocity approaches the speed of light, time appears to slow down for that object from the perspective of a stationary observer. This effect has been demonstrated and verified in experiments involving high-speed particles and atomic clocks.
On the other hand, time dilation due to gravity, often referred to as gravitational time dilation, occurs when there is a difference in gravitational potential between two points in space. In the presence of a massive object such as a planet or a black hole, time runs slower for an observer in a stronger gravitational field compared to an observer in a weaker field.
Both forms of time dilation have been observed and measured in various experiments and observations, including the famous Hafele-Keating experiment that confirmed time dilation due to velocity. The effects are not illusory or recording mistakes but fundamental consequences of the nature of spacetime and the way it behaves according to the theory of relativity.