Speech recognition is more related to recognizing words or phrases, while voice recognition can be more related to detecting who is the person speaking or if the audio detected is a human voice instead of any other noise like a car, etc...
in speech recognition spoken text is the object. In voice recognition the voice of speech is subject of analysis. For analyses purposes both are handled differently.
Processes and methods of converting speech to digital data is Speech recognition . Where as voice recognition is more about who is speaking ( person identification) .