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You are getting into details that I am not concerned about.
I am talking about the ethnic Jew as a race as opposed to
the religious Jew.

The ethnic Jew can be any religion that he/she wishes but
they are still a Jew.

The religious Jew can be of any ethnic group and convert to
being a Jew.

I know that there are various things that one group may or
may not do as far as religion is concerned. But my point is
in answer to the question is that a Jew can be either or both.

My problem was for years that a Jew was of a religion. However
somewhere back there in my head I also knew that it was also
ethnic.

These are two separate things operating under the same name
which has caused me so much confusion and it appears
confusion for many others.

I'm not sure why you are concerned about putting people into your categories. Your system may make sense to you, but it is irrelevant to observant Jews.

Jews -- at least religious ones -- don't believe that there is anything to your concept of the "ethnic Jew". That concept, which is the basis for Israel's Law of Return, exists only because non-Jews (Hitler) imposed it. (The turn-of-the-century mayor of Vienna, Karl Lueger, was famous for imposing anti-Jewish laws but associating with people who, under his rules, were "Jews." He famously retorted, "I'll decide who is a Jew.")

To religious Jews, a Jew is someone who's mother was Jewish (according to Jewish law) or who converts to Judaism (according to Jewish law).

Religious Jews would not feel a strong ethnic affinity to someone who's father was Jewish but who's mother was not Jewish (unless that person converted to Judaism).

My problem was for years that a Jew was of a religion. However
somewhere back there in my head I also knew that it was also
ethnic.

There is no ethnic Jew. The term is probably used by a person born or raised of Jews who is eschewing any religious feeling while at the same time unwilling to swear off all traces of heritage, ie a "fallen" Jew.

Being an "ethnic" Jew is the same as saying you are from California and like the beach. It is a willing embrace of some aspect of Jewish culture. But which culture? Since Jews come from all over the world the cultures vary as well though there are universals.