For example, the word "jihad." Translated, the word means "struggle" or "strive" and I am sure there are others. The word "jihad," is just taking the pronunciation of the word in the native tongue, and spelling it phonetically in English. Is there a specific word for that?
That practice is called transcription:
1.2 A form in which a speech sound or a foreign character is represented:
Transliteration is not necessarily a phonetic operation:
Write or print (a letter or word) using the closest corresponding letters of a different alphabet or language:
Because Arabic has a dissimilar alphabet system, جهاد ǧihād [dʒiˈhæːd] comes across as a phonetic transliteration, which is technically transcription.
There are specific principles of transcription applied to each language separatey.