Kaithi is Brahmi-derived, descended from Nagari. Because of the fuzziness in when Bengali split from Nagari, it’s not really clear whether to say if Kaithi is descended from Bengali or from Nagari; this means Kaithi is either sibling to Devanagari or niece/nephew to it.
Both Gujarati and Kaithi are normally written without a headline. However, Kaithi sometimes uses a headline for emphasis, particularly of titles, in much the same way that English uses underlines.
Like Gujarati, Kaithi was used for practical matters, but instead of being used by merchants, it was originally used by governmental scribes in North India. These scribes filled a niche filled today by stenographers and photocopiers. Both the merchants using Gujarati and the scribes using Kaithi were interested in writing quickly, so losing the headline might have been parallel discoveries of a way to save time, or perhaps Kaithi was influenced by Gujarati.
Kaithi was used widely in northeastern India in the 1600-2000 AD timeframe, used to write many spoken languages. In 1875, two British-run areas — Bihar and the North-Western Provinces & Oudh — standardized the Kaithi script and used it for administrative purposes. In the 20th century, however, it was displaced by the growing popularity of Devanagari in India. It persisted for some time — and in fact might still persist — in the Indian diaspora community for private use.
Kaithi used word separators and sentence separators, but inconsistently. Usually the word separator was something that looked like a ‘-‘; usually the sentence separator looked like an “=”.
Kaithi scribes also sometimes used a “danda”, a form of punctuation common to most Indic scripts. The single danda is a vertical bar in most scripts used to separate sentences much like the “.” in Latinate writing systems. A double danda was used to delimit the ends of verses. (Kaithi is slightly unusual among Brahmic scripts in that its danda has serifs at the top and bottom.)