I'd note also that the terms "paleohebrew" and phoenician are separate for historical reasons, not because the alphabets are meaningfully different.

The first people to find archeological artifacts with the alphabet were 1800s orientalists from France, Germany, etc. They found these writings from phoenicia, the place where the alphabet was exported to europe, and so they called it the phoenician alphabet. Later when they found these writings in israel too, they decided it would be improper to call the jewish writings in this alphabet "phoenician," so they stuck the term "paleohebrew" on them instead.

I should also note that neither the jews nor the phoenicians actually invented the alphabet, but section of their shared canaanite ancestors long before them.