It's not clear what you are asking. I'll clarify some terms and describe the generally accepted meanings which apply-
The terms near-field
describe different acoustic regions based on distance from the source and room size. The free-field (or near-field) is where the sound arriving directly from the source is dominant, the diffuse-field (or far-field) is where the sound arriving from all directions in combination is louder than the direct sound from the source. Although the concepts are more or less interchangeable, the terms near/far-field
is typically used when talking about reproduction, monitoring, and PA reinforcement. The terms free/diffuse-field
are typically used when talking about the original soundfield and the placement of microphones.
The demarcation between those close
regions, where the direct and diffuse sound components are equally loud, is called the critical distance,
or reverberation radius
and is considered a generally optimal place for a stereo pair of microphones intended to make a well-balanced recording of a source "as it sounds in the room". A closer position will sound more dry and direct (appropriate for "close-mic'ing", as done for PA reinforcement or isolated multi-track recording), and a farther position more reverberant. Most AUD positions are back in the diffuse-field region with respect to radiation from the instruments themselves on stage. A recording position which is on-stage or at the stage-lip is likely to be close to the critical distance. A directional PA changes that by projecting it's near-field region into the room along it's primary axis, so with respect to the PA the critical distance is usually a few rows back. Still, most AUDs are made from back in the far-field region of the PA, whereas stack-tape is made up close in the near-field region of the PA.
When microphones are described as "free-field response" or "free-field equalized" verses "diffuse-field response or equalized" that describes the frequency response of the mic as being intended for recording from up close or from further away. Omnis are more frequently described in this way. A free-field omni is flatter when measured on-axis at a standard measurement distance of typically one meter. A diffuse field omni measured at the same one meter distance will have an increased sensitivity bump in it's response curve at high frequencies, which compensates for both the attenuation of high-frequencies in the direct sound due to increased distance and the frequency response of diffuse sound (that which has bounced around the room and arrives from essentially all directions with equal energy) which has less high frequency energy due to the high frequencies being more easily absorbed by the room surfaces and all the other stuff in the room.
Take the Schoeps omni capsules as an excellent example. Schoeps offers four different omnis which vary in response from free-field through diffuse-field. Look at the differences in the response curves of these omni capsules when both are 1 meter from the source (the images and description in italics below are from Schoeps' website
First the MK2 at the near/free-field end of the spectrum, which Schoeps describes as-"omnidirectional pattern
very flat frequency response
corrected for a free sound field
for use close to the sound source (frontal sound)
often preferred for relatively close miking of instruments, vocalists, etc.
This capsule type has a flat frequency response for frontal sound incidence. This yields a very natural sound when recordings are made within the reverberation radius, where the direct sound (frontal incidence) predominates over the reverberant sound (random angles of incidence)."
..and compare that with the MK2XS, at the far/diffuse-field end of the spectrum, which Schoeps describes as-"omnidirectional pattern
for miking distances at which the predominant sound is no longer direct
useful for relatively distant placement in reverberant environments.
The MK 2XS (formerly 3) is designed for placement in a diffuse sound field, i.e. at distances in reverberant environments where the greater portion of arriving sound has already been reflected from various room surfaces. In such placement the integrated frequency response of this capsule is essentially flat; the on-axis high-frequency response elevation shown in the graph below is not heard as such."
With respect to a cardioid mic, in addition to the high-frequency response differences, the inherent low-frequency cardioid roll-off and related proximity effect also come into play. A cardioid appropriate for nearfield use may have less low-frequency sensitivity, which gets compensated for by proximity effect and close placement to the source, resulting in a flatter response at it's intended recording distance. The response of a cardioid appropriate for use at far-field distances generally will have "more bass" so it doesn't sound thin when used well beyond it's proximity effect range, perhaps in combination with a high frequency lift. Cardioids are not typically referred to as "free-field" or "diffuse-field" response like omnis are, probably because their behavior varies in a more complex way, based not just on critical distance but also proximity effect.