"Current" and "present": understanding the distinction

What is similar?
Both "current" and "present" can refer to something happening now or existing at this moment in time.
What is different?
The word "current" often implies a more temporal and ongoing situation, like a trend or event, and can also refer to a flow of water or electricity. "Present" can refer to something existing now or being in a particular place and can also mean a gift.
Which one is more common?

Examples of usage
Current- The current CEO is planning to retire next year.
- The current flows swiftly through the river.
- Our current project is due next month.
- I am happy to be present at the event.
- The present situation is quite challenging.
- She gave me a beautiful present for my birthday.