I know that quatrains are called pAdas in Sanskrit. But what is the technical term for couplets in Sanskrit? I'm having lots of trouble identifying this.
The most common name in Sanskrit is śloka (श्लोक). A single śloka contains 2 lines of Sanskrit text, usually consisting of an equal amount of syllables. Lots of Sanskrit poetic works contain only a single meter for their śokas, but there are many kinds of meters and multiple can be used by a single work.
In order to understand the anatomy of a śloka, such as what is meant by pāda (or, ‘foot’), you can look at various pages on the internet, such as wikipedia
The śloka is treated as a couplet. Each hemistich (half-verse) of 16 syllables, composed of two pādas of eight syllables, can take either a pathyā ("normal") form or one of several vipulā ("extended") forms.
Update: according to the Nāṭyaśāstra 15.89-90, an authorative work on prosody, a couplet is termed ''sampad'' (alternative spelling ''sampat''):
“A couplet in which the number of syllables is neither in excess nor wanting is called a regular one (sampat).”