Ghetto=Slum?

It is sometimes used that way, but I suggest you don't. Originally an area in Europe to which Jews were confined, ghetto is now applied to about any ethnic neighborhood. Slum describes an area of poverty and disrepair. In other words, some ghettos are slums, and some slums are also ghettos, but the terms are not really interchangeable.

Then can we use "ethnic district" or "ethnic settlement" to substitue ghetto?

Yes.

And latinos speak of the "barrio".

One important difference in the above: The ghetto was usually imposed on people who had to live there, by law, decree or whatever. It was enforced.

The other areas you name are usually places of choice for their inhabitants, to live among their own kind, or in the case of "slum", because they can't afford anything better.

In NYC a politically correct term, I believe is "inner city." This, I believe, implies an area that may have once been the neighborhood of white ethnics, and today is a community of people of color. It might have very good housing stock; no slum at all. Not even a ghetto, since today people of color do live in many neighborhoods that are not predominantly communities of people of color. So, the fact that an "inner city neighborhood" is a community of people of color can just be a self-imposed segregation of sorts, I believe.

I think "inner city" implies the neighborhoods that might be thought of as not particularly friendly to whites. Also, where the police might feel that some of the younger people of the community could have an attitude towards the police.

Ghetto is originaly an European term
Slum is a North American term
Both are 20th century terms
I don't know the current politicaly correct term to use these days
If you use "ethnic" as a substitute? Well what about the middle class "ethnic" neighborhood I live in?
Go to WIKI is my advice

You have chinatown, little Italy, little India, Koreatown, Japantown, etc.

Suppose we use "ethnic district" as a superordinate term (or umbrella term?) to cover all the names you have mentioned where people of different ethnicity live?

I don't think so. If there's a number of different ethnics represented, wouldn't it just be called a neighborhood?

Most go for the food, DVDs, books and maybe some clothing. Of course it is usually the first and second generation go there.