They both come from the Phoenician alphabet, which had the same letters and the same order. It's a very ancient writing system, and most of the abjads that are similar are not used anymore. Even Greek is ordered similarly, but they cleverly added vowels, and eventually that alphabet ended up as the Latin alphabet most languages use today.

Fun fact: The Hebrew alphabet isn't actually Hebrew, it's Aramaic, which everyone spoke way back when. The Hebrews adapted the script to their language and used it to write a rather popular book, while Aramaic fell out of favor when the Greeks came and starting kicking butt and taking over.

The writing that the Hebrews originally used look like this: https://www.ancient-hebrew.org/files/alphabet_chart.gif

If you mean Biblical Hebrew yes. The most letters are the same :)