This is what I believe they are but I am not a 100% sure:
IT Managed Services: A company has their services in house and an IT company "managed" them remotely. Normally under a long term contract.
IT Solutions: A company needs a "solution" to resolve a problem and an IT company implements the solution . Normally under a short term contract or project. The IT company is not responsible for the management of the solution.
IT Consulting: A company needs a solution and an IT company looks around for the best one but does not implement it, nor manage it.
Am I right?