Intellect is the name of an “ability”. Rationality is an “approach”.
Intellect is the ability of mind that it can store, manipulate, organize and suitably utilize past sensory information. Mind organizes sensory information due to the application of intellect. Knowledge is so organized information.
Rationality is an ideological approach whereby you show confidence in ability of human mind (intellect) that it can lead to truth. In other words, Rationality means using the faculty of intellect with confidence.
