Thinking of those two things as distinct concepts with clear borders is a mistake. Both religious and ethnic group do not usually have definite boundaries and they are not always seperate from each other. Saying Arabs when you mean Muslim is what you mean is indeed a mistake. Most Muslims are not Arabs, but that proves nothing about how to classify these things.
Hebrews is a different issue. Jewish is actually Judah-ite, from the tribe of Judah. These were (according to the tradition) the surviving tribe of the Israelites or People of Israel. People is actually a bit misleading. In Hebrew it uses the word normally translated as 'Nation'. In modern times, the relationship between Judah & Jewish has been blurred since some groups trace their heritage to other (lost) tribes.
In any case, all of these equally refer to an ethnic group though you could argue that they are not exact synonyms. This is not just about the origin of the words. It is also the religious tradition. Jewish is not a Religion in the sense that Islam or Christianity are. It are not something you chose. It is not something you can stop and it is not something that anybody who is not (ethnically) Jewish is required or encouraged to join. Basically, the "religion" as you would probably call it doesn't distinguish between religion and ethnic group. The members of this ethnic-religious do not usually do so either. That is, many secular, atheist Jews describe themselves as Jewish, and behave in someway that indicates this.
Hebrews & Israelites, People of Israel, are as far a I know, used interchangeably in the old testament. In modern Hebrew all but the most pedantic (and religious) will use Israelites interchangeably with Jews. Secular Jews are unlikely to say Jews. "Hebrews" is not really used in modern Hebrew unless making some sort of biblical reference. In some languages it has a derogatory ring but in some languages describing someone as a Jew/Hebrew/Israelite is derogatory regardless of the word you use.