A modern orchestra is a group with a core majority of string instruments (violins, violas, celli, and basses). A symphony orchestra is typically a large string group with a few of each wind and brass instruments added, along with a percussion section. Typical instrumentation has a wind section of two to four oboes, flutes, clarinets, bassoons, trumpets, french horns, trombones, and one tuba. A percussion section is staffed with about a half dozen people. A typical professional orchestra will have a harp player or two on staff, as well as someone who plays piano.
A school band, military band, marching band, concert band, symphonic band, or jazz band typically has no string instruments, and if there are string instruments in any of these groups, it is an exception rather than a rule. Some of these bands include instruments not found in an orchestra. Saxophones, baritone horns (or euphonium), and sousaphones are expamples of these.
I don't understand the confusion here in Texas, as a band and orchestra are two distinctly different entities. Where I am from, a band director would not dare to call himself an orchestra director, nor would an orchestra director call himself a band director (kind of a little war they have going there). We cringe at such things... lol
In inner-city Birmingham, I was simply known as the "string-man". That's an entirely different story.
As for the difference in teaching band and orchestra, you do need to use different techniques. A band teacher needs to be able to tell what is happening in a student's mouth, and be able to recognize what he cannot see. A string teacher has everything out in front of him and can easily see when a student needs to work on technique. Other than that, music is music. A talented musician and teacher can teach band, choir and orchestra equally well if he so desires.