Hora is a word with several different meanings.
Hora means time. The Sanskrit word appears in ancient Greek and Latin language, too. The english word hour and ancient Greek hora are borrowed from these sources.
This is also the meaning of the Hora explained below.
Hora is the Varga of division two (D-2). There are only 2 possible Horas, the Hora of the Sun (assigned to Leo) and the Hora of the Moon (assigned to Cancer).
Kalyana Varma's Saravali explains the word Hora as derived from Ahoratra. Ahoratra means the span between day and night. Removal of the first and last syllable from that word yields the word Hora.
Day stands for the Sun, night stands for the Moon. The Sun rules the 12 zodiacal signs. The Moon rules the 27 Nakshatras.
So Hora is the science that deals with the 12 Rasis. That's what Saravali is about. There is no discussion of Nakshatras in that scipture.
Parasara explains the meaning of Hora in the illustrious Hora Shastra (3-7) as
Details of Nakshatras have to be understood by other scriptures, while I narrate to you about the effects of Grahas and Rasis.
So Hora is the science of Grahas (planets) in Rasis (zodiacal signs).