Yes and no. There is no “frame-rate” in audio recorders. There IS a “Sample-Rate” which is the audio equivalent. For example your video frame-rate is 25 of 30 or 50 or 60 FPS (or the slightly lower “NTSC” rate like 29.97, etc.)
But the standard audio SAMPLE-RATE is 48 thousand samples (48K) per second, regardless of the video frame rate.
IMHO, the three most critical things in selecting a separate audio recorder are:
1) Sample-rate accuracy. If you have a combination of audio recorder and video camera that don’t match with reasonable accuracy, you will be slipping out of sync in a matter of a few minutes. This may not be a problem for short shots. Or even for longer shots where you will be intercutting “B-roll” video clips or maybe be even for shots where lip-sync is not important. If the dialog is “voice-over” narration or you are doing “over the shoulder” shots where you can’t see the subjects lips, etc.
2) Sample-rate selection. My very strong preference would be for a recorder that allows 48 KHz sample rate. Most low-cost recorders use the slightly slower 44.1 KHz or even lower for simple utility “voice recorders”. Now, you can re-sample audio from 44.1K up to 48K, and some video editing software even does this for you. But any time you have to re-sample something means a potential loss of quality. Not to mention the extra time it takes.
3) Data compression. I would have a very strong preference for an audio recorder that will store the audio as UN-compressed WAV (or AIFF, etc.) files, and NOT MP3 or other kinds of compressed format. Any time you have to un-compress something (in order to edit it), and then re-compress something (for distribution), you run a significant risk of loss of quality. In extreme cases, rendering audio that is unusable.