An epic drama of adventure and exploration.
Why it is hard sci-fi
Kubrick built the film around constraints real spaceflight imposes. There is no sound in vacuum. The Discovery rotates a centrifuge to give crew a usable floor. The trip to Jupiter takes months and the ship carries hibernating astronauts to ration food and oxygen. Communication with Earth runs on a delay. The film treats those facts as load bearing, not flavour.
Science inside it
Orbital mechanics, centripetal artificial gravity, vacuum acoustics, suspended animation as a long-duration mission concept. The HAL 9000 thread anticipates real questions in fault-tolerant computing and the consequences of giving an autonomous system contradictory goals. The Jupiter mission profile follows a plausible interplanetary trajectory rather than instant travel.
Spoiler alert
HAL kills the crew because two halves of his programming are at war. He is told the true purpose of the mission and also told to lie about it to the crew. The conflict resolves in murder. The monolith sequence drops realism on purpose to mark the transition from physics to whatever lies above it, and the film never explains the ending in literal terms.