These samples are somewhere 'inbetween' the samples of the receiver sample clock.
No. They aren't "in between". You are moving the reference clock remember. You get to decide where "now" is.
If I record a 48K wave file and give it to you and you play it at 48.001kHz. It will sound slightly higher pitched, but a tiny fraction of a percent and far beyond any tuning tolerances of any instrument.... and it will play in a slightly shorter time. 0.00000.... whatever %.
All the samples are the same. Nothing is interpolated.
If you are going UP in sample rate, you can interpolate with a LPF. If you want going DOWN sample rate you can anti-alias. But like for like, there is no "in between".
EDIT: What I think you may be confusing is a full Digital to Analog back to Digital resample, which to be honest is just ... why would you go through the two most lossful and distortion/noise inducing steps when you don't have to?
A composer sets a challenge of writing music with a 120bpm tempo. He gives it to an orchestra and asks them to play it for him at 120bpm. Now because the conductor is human and not totally precise the orchestra may be playing at 121bpm sometimes and 119 other times. Over the full performance the length of the composition might change by a few seconds or a few minutes. It does not detract from the performance and it's unlikely even the composer noticed.
If however you took two orchestras and gave them the same music, the same rate, 120bpm and put them in two concert halls beside each other. The two orchestra's would not stay in sync. Their timing would drift forward and back or one might play the whole set slightly faster and finish 5 minutes early.
If the composer was feeding the conductor sheets of music at exactly 120bpm and the orchestra played at 121bpm, the conductor would run out of music.
If you want the two orchestras to play in sync, you need to do other things to bring them into sync. Either artificially in post (like in the real world), or by using synchroniser lights of even hand signals. There are examples of VERY large multi band drum offs and the science behind how the syncing actually works is pretty amazing.