Depending on how specific you choose to be, different parts of term "total internal reflection" are redundant, incorrect, and lacking in meaning. Some of this may be due to misapplied meanings. But then, many terms here involved get misused habitually, so I'd like to clarify them.
Three or four things can happen (in classical optics) when light traveling in one medium encounters the boundary with another. They are diffuse reflection, spectral reflection, absorption, and transmission. Since we are considering materials transmission and spectral reflection can happen, diffuse reflection really isn't under consideration. I just include it to be complete, but I'll number it as a zero.
Diffuse reflection. The light bounces back into the original medium in more-or-less random directions.
Spectral reflection. The light bounces back into the original medium according to the Law of Reflection.
Absorption. The light's energy is absorbed into the materials as heat.
Transmission. The light passes into the second medium according to the Law of Refraction (Snell's Law). "Refraction" means the change in the path of the light, not the fact that it passes between the media. Since it is necessary, some confuse it for "transmission."
Two of these three always happen, even in minute amounts. The one that sometimes won't happen, is transmission. If the light is passing from a dense medium to a sparse medium, there are geometries where there is no solution to the Law of Refraction. In such cases, transmission does not occur.
In the term:
"Total" seems to imply that all of the light reflects. Yet some gets absorbed, so this interpretation is incorrect. In fact, as another said, it means that all of the light that continues past the boundary is reflected.
"Internal" is a puzzlement to me. Does it mean "inside of an object?" There is nothing about being inside of an object that links it to TIR, except that most of the time such an object is denser than the medium around it. But the most common instance of TIR is what makes air bubbles in water appear shiny, and the reflection is occurring on the outside surface of the bubble. Or, does it mean "light stays inside the first medium?" That is what "reflection" means, so it would be redundant. So the word seems to lack a meaning.
And I have a good reason to point out all of this. Rainbows are often attributed to TIR, yet it is impossible in spherical raindrops. It is impossible because the angle of incidence inside the drop is equal to the angle of refraction as the light entered the drop. This angle is, by definition, less than the critical angle. The effect is caused by reflections that occur inside the drops, but "internal" carries no special significance.