^ what is the difference between them and how are they ?
Construction Management/Construction Project Management are pretty much similar. It's a good profession to break into, however that's mainly because the construction market is booming. Whether it remains this was long term seems unlikely.
Project Management is a broader field which covers projects across all sectors. I really enjoyed project based work when I was with the government, however, given the nature of projects permanent employment is hard to come by. It's something Id do if I had a permanent job with a large MNC/government department and I wanted to diversify my skill base.