Sign language interpreting
Signed-spoken interpreting is a live translation from one language into another language in either signed or spoken language. Regardless of the mediums, both languages are different -- languages of their own. E.g. ASL and English are two distinct languages, independent of each other.
There are two types of interpreters. One is a hearing certified interpreter whose native language is usually the spoken language (e.g. English) and the second language is ASL. The other type is bilingual Deaf certified interpreter whose native language is ASL.
An example of a certified Deaf interpreter is Jonathan Lamberton, NYC deaf interpreter, who went viral on news when he was interpreting into authentic ASL during Mayor de Blasio's winter weather briefings in January 2015.
Another example, a Deaf interpreter translates from the live captioned English on the laptop into native ASL for a Deaf student in a classroom.
Understanding the difference between simultaneous and consecutive interpreting
Finton, Lynn; Smith, Richard. Interpreter Discourse: English to ASL Expansion / ASL to English Compression. Rochester Institute of Technology.
Taylor, Marty M., PhD (1993). Interpretation Skills: English to American Sign Language. Interpreting Consolidated, Canada.
Humphreys, Linday. The Professional Sign Language Interpreter's Handbook.
Metzger, Melanie. Sign Language Interpreting: Deconstructing the Myth of Neutrality. Gallaudet University Press.
Patrie, Carol J. Phd. Series: Interpreting in Insurance Settings., Interpreting in Legal Settings., Interpreting in Medical Settings., Translating from English, Consecutive Interpreting from English, Simultaneous Interpreting from English.