In general, a bishop sleeve is full from top to bottom, and the bottom brought in close to the arm to finish but it’s not tight along the length of the sleeve. A gigot is the large puff then tight/form-fitting on the arm below the puff. The bottom two of the 1893 Groupe de Manches are bishop variations; the right dress of 1893 Promenade Toilettes shows bishop style. Then, 1891 L’Art et la Mode is a bishop style, as are both from 1891 from Le Moniteur de la Mode.

Depends on the era/time period. Is your pattern for 1890s? For that decade I’d think “modesty sleeves” are the inside, fitted sleeve lining where the outer fashion fabric is gathered/pleated and mounted to over the lining ones. But not entires sure here. If for mid-19th Century, I’d say they are the undersleeves that fill in the wide bell fashion sleeves.

We’ll see a variety of construction techniques for holding out those huge sleeves. Many were underlined with stiff fabric such as organdy, tarlatan, or other stiff mesh type of textiles. I don’t believe I’ve ever heard of starching bodices, only the undergarments. Ruffles could be applied on the inside of the sleeve, between the fitted inner sleeve and the puffed outer one to hold the shape. Although not used often, small stuffed pads could be sewn into the sleeve head as well.