Vinyl Ripping To Digital Voice Recorder

I’m in the process of recording and ripping some records to MP3 using a digital voice recorder. Can somebody tell me if there is any difference in terms of quality between recording from a cable coming out of the headphone socket as opposed to phono out on the mixer?

It depends on the equipment that you are using.
Note that there is always some loss of sound quality when compressing audio to MP3 format. For best quality you need to keep the audio in an uncompressed format such as WAV or FLAC.

I don’t mean in relation to the target file type so to speak. I mean say if I did 2 recordings of the same vinyl, one via phono rec out from the back of the mixer, and one via the headphone jack out, would they both be the same quality? Are they both just stereo outs via different cables?

As I said, it depends on the hardware, but usually the headphone output goes through an extra headphone amplifier circuit, so it may be of lesser quality than the main Record output. There may also be other differences in the signal routing. The “Tape” / “Record” out is the one that is intended for recording.

Line or show output is intended to present the best possible performance to the audience. The headphone output is generally designed to be loud. Trying to mix in a busy booth is generally not a good time to worry about subtleties of music gradation – unless you’re mixing Vivaldi.

If there is no booth it’s even more important for the headphones to be loud at the expense of everything else.