The two instruments you see depicted are roughly contemporaries (the Bass Trombone is actually a little later, in the 1910’s, and English rather than American, but contemporaries they are just fine enough).
Traditionally beginning in the Renaissance, instruments were organized in groups called Consorts, with different voices within each family taken up by different sized versions of the same instrument. At that time, it was not likely that specific instructions were given as to which instruments should play which piece, so pieces typically ended up in several parts, a high part, a mid part, a low part, and a bass part, for example. We are familiar with this today, with the SATB form of choral music. The trombone, or sackbut, as its period ancestor was called by the English, likewise took the form of a consort, specifically, an alto, a tenor, and a bass, and, arguably, a contrabass, and, hypothetically, a soprano. Some believe that typically, the trombones functioned as part of what is called a broken consort, in which multiple instruments or instrument families are mixed to fulfill all the voices, in this case, often borrowing the soprano-voiced cornetto to fill in the soprano part, combined with an alto (F or Eb), a tenor (Bb), and a bass (G, F, or Eb) sackbut.
While this habit of consorts slowly died out through the Classical and Romantic periods as greater instruction and a broader reliance on fixed-instrumentation “orchestras”, we can see some remnants today, for example, Soprano, Alto, Tenor, Baritone (and occasionally Bass) Saxophones are readily available and played by hundreds of thousands of musicians around the world. We also see Bassoons and Contrabassons, although the tenor and alto voices of that family have long ago disappeared into obscurity. We have Eb Bass Tubas and Bb (technically, Great) Bass Tubas paired with the Tenor Tuba, best known for its little featurette in Holst’s The Planets, Mvt. 1 (Mars). We have Eb “Sopranino”, Bb “Soprano”, Eb Alto, and Bb Bass clarinets, although only the second and fourth appear with any regularity.
Unfortunately, the trombone is not so much one of those lucky instruments with an intact consort. With the invention of rotary valves, it was possible to allow a modified tenor trombone to play (most of) the bass parts. The instruments we call bass trombones today are really acoustically not bass trombones if we go by consort standards, not by range or typical parts, but glorified enlarged tenor trombones with some range-extending valves to permit playing in and around the pedal range. Alto trombones, as with almost all alto brass, more or less died out with the end of the popularity of brass bands, at least in the United States.
A good practical application from this survey: when orchestrating, remember that instruments typically occur and function as families. While families may not be true consorts of SATB instruments any more, the modern families of orchestral instruments have, for the most part, formed broken consorts that can function as SATB or other vocal settings. Think of how you can use families to contrast, reinforce, or accompany each other in interesting ways through your piece, and how treating families as units can help keep the orchestration and composition from becoming too busy.
Disclaimer: the content of this essay is for entertainment purposes only. I am not and do not claim to be in any way an expert on any of the subjects discussed, only a keen student with some broad interests and a willingness to share my interest.