Growing up, my father listened to big band music. These bands are usually referred to as "Glenn Miller and his orchestra" Or "Paul Schaeffer and the CBS Orchestra". Is it that an orchestra has strings? What is the primary reasoning to calling a group of musicians a band, or orchestra?
The main difference between an orchestra and a "band" has a "leader" an orchestra has a "conductor". Note that a conductor does not play an instrument, whereas a leader does.
Generally, the distinction is between a "military band" and a "symphony orchestra", historically the two most common types of large instrumental ensembles. The major difference between those two is that a military band has no stringed instruments (with the possible exception of double bass), instead replacing that area of the sonic space with additional woodwinds and brass. While a 60-member orchestra may only have two or three each of flutes, clarinets, trumpets and horns, a 60-member military band might have as many as eight of each, especially of woodwinds. The term "brass band" is largely synonymous with "military band", while "brass choir" or "wind ensemble" generally implies an ensemble made up more exclusively of brass or woodwind instruments (though "wind ensemble" is often used academically to refer to smaller groups of mixed brass/woodwind).
In the wider sense, "orchestra" generally implies a wider range of instruments, and probably of members, than a "band", even if the terms aren't used in the context of the previous paragraph. "Orchestra" also usually evokes images of a more sophisticated style of music, while "band" implies a more "pop culture" ensemble. However, depending on other qualifiers used to describe the group, the terms "band", "orchestra" and more generic "ensemble" have been used almost completely interchangeably.
Small ensembles in the pop and folk idiom can all go by the term of band; this answer will focus on what are referred to as "large ensembles."
In the jazz context, the name of orchestra was historically applied in order to give credence to groups that would otherwise have been marginalized by the cultural mainstream and racism. That term has now been accepted in the jazz tradition. It's possible that "band" originally referred to the military groups that jazz ensemble playing grew out of, and "orchestra" was seen to apply to a higher standard of musicianship. Outside of the jazz context, there are a few more rules that apply:
Orchestra generally refers to any ensemble with sections of bowed string instruments. This can be further broken down into String Orchestra to include only the stringed instruments, and Symphony Orchestra incorporating winds and percussion.
Band, outside the idiom of folk and pop music, generally refers to an ensemble of wind instruments plus percussion section, with or without a string bass. Brass Bands are mostly popular in Europe, and contain the above without woodwind instruments. For those ensembles that include woodwinds, there exist other terms of questionable interchangeability: Concert Band and Symphonic Band are generally used in school music programs with too many musicians for a single ensemble (Typically, the Symphonic Band is held to a higher level of performance than the Concert Band). Additionally, Wind Ensemble is usually held to the highest level of performance, and in most cases contain only one player per part.
To attempt to draw some questionable generalization from this, I might say that the distinction between Band and Ensemble is that of number of players per part. This holds true to jazz in many educational situations: in a music program with more than one jazz group, the Jazz Band might have many musicians per part, while the Jazz Ensemble would be the auditioned, one-on-a-part ensemble.
In the orchestral situation, string instruments are always many-on-a-part for purposes of volume, and orchestral wind sections are almost always one-on-a-part.
Of course, all of this is just an attempt to generalize tradition. Really, the only answer to your question is "because that's what they call themselves."
Just to briefly elaborate on the term Jazz Orchestra... Nowadays this term is interchangeable with Big Band, the instrumentation of which is fairly standardized:
Common variations include vibes, auxiliary percussionist, and/or extra trumpet player. Soloists (traditionally 1st tenor sax, 2nd trombone, and 4th trumpet) are generally seated closest to the rhythm section. Section leaders sit next to them (thus they are all stacked and can hear each other clearly), and remaining parts are sequential down the line, allowing the bass voices (bari sax, 4th trombone, and upright bass) to border the band.
Band is a very imprecise term. Many swing bands contain stringed instruments (Double Bass obviously or Bass Guitar) and some have contained string sections. Pop bands can contain almost anything.
Orchestras can contain almost anything as well, but pretty much but tend to be
In symphonic situations. Philharmonics tend to be bigger, can sometimes incorporate keyboards (I think, piano and the like). Chamber Orchestras tend to be strings with keyboard often (which was usually a harpsichord so technically that would be a string instrument) often wind and sometimes brass (french horns etc).
They are not exact terms really and their definitions can be stretched somewhat.