Semitic is language descriptor, not racial or cultural. Your examples indicate this. Would be expected that Arabs and Jews, the first and third practitioners of semitic languages today would share cultural similarities.
No, not necessarily cultural. Ishmael after all was a hybrid of Semite (through Abraham) and Hamite (through his Egyptian mother Hagar).
And there are plenty of semantic differences between Arabic and Hebrew. Take the word “akbar”, which apparently in Arabic means “great(er)” (such as in “Allahu Akbar”); but the Hebrew word “akbar” means “mouse”.