What is it called when two singers sing together, but one of them on a lower scale but the other on relatively higher? Is it still harmony?

Two people singing together is called a duet. If they're singing the same notes, they're singing in unison. If they're singing two parts, they're singing in harmony. One is singing the melody while the second voice is harmonizing.

It's called a duet. If they're singing harmony, then it's called "harmonizing". If they aren't, then it isn't.

It's called singing in harmony.

They're duets and, yes, they are singing harmony. Whenever two singers sing different parts, one singing notes above or below the other in pitch so as to form musical chords (as opposed to singing the same part by both singing notes at the same pitch) that's vocal harmony. 

What you often hear in churches where everyone's singing the same melodic line for a hymn, that's not harmony. It becomes harmony when the men, for example, instead sing the words along with the bass line, which appears in the notes printed below the words in the hymnal, rather than everyone singing along with the melody line, which appears in the notes printed above the words in the hymnal. 

You’re right.  That’s an example of two singers singing in harmony.  A song is written in a certain key, and that key has certain notes.  A melody uses those notes and is what your ear hears as the main voice.  Someone can sing in harmony with them, usually a bit higher or a bit lower.  Either way is harmony: a main melody and another singer higher or lower.

   There can be more than two!  There can be three, four or even five simultaneous vocalists, all singing different notes together.  (The Eagles were famous for their spectacular five part harmonies)  

   If you listen to a piano or guitar playing a chord (several notes together that sound nice) those are secondary notes that the harmony vocalist chooses from.   

   There are technical terms for all this, but this is the easiest way to understand it.

As long as they sing in a fixed proportion like an octave or so many semitones apart, it's harmony. Think of it a bit like two-note chords.

They could change at points in the song, as long as the variations are just not random times and shifts.