If you are carefree, you do not have any cares or worries and therefore feel happy and able to enjoy life.

1. Before her marriage she had been lively and alert and carefree.
2. He was aware of a glorious carefree feeling of joy.

If you are careless, you do something badly because you are not giving enough attention to it.

3. …if your courier is careless and leaves the coach unlocked.
4. He was careless and inefficient and drank too much.

If you are careful, you do things properly and with a lot of attention. Careful is the opposite of careless.

5. I showered slowly, being careful not to wet my sore face.
6. He watched all this with the most careful attention.