I'm thinking about it in terms of photon waves intersecting, and electrons moving throughout the antenna resonating back and forth.
Let's start by setting aside photon waves and the movement of individual electrons. These are indeed accurate models of RF phenomena, but they're far too detailed and make it difficult to see the signal processing that's going on. We can simply deal with the signals themselves, either as explicit descriptions of sine waves, or as a spectrum in the frequency domain.
For example, I have a 6.7KHz wave, and a 100KHz carrier wave together. How does the proceeding electronics tell the difference between that signal/carrier pair, vs just a 6.7KHz and 100KHz wave that just happened to play at the same time? Is there even a way to tell?
Carriers don't "carry" a wave through space in a certain direction. Instead, they "carry" a wave through the frequency domain, in a sense.
Let's assume you're using amplitude modulation. If you are transmitting a 6.7 kHz signal with a 100 kHz carrier, you aren't emitting 6.7 kHz and 100 kHz at the same time out the same antenna.
Instead, you would take your 100 kHz local oscillator and your 6.7 kHz signal, and you'd feed them into an RF mixer, which is just a circuit that's good at multiplying RF signals.
With a bit of mathematical analysis, we can show that multiplying two sine waves at frequencies \$f_1\$ and \$f_2\$ produces sine components at frequencies \$f_1 + f_2\$ and \$f_1 - f_2\$. In the simplest case (double-sideband, transmitted carrier), the mixer emits 106.7 kHz and 93.3 kHz as well as a carrier at 100 kHz. This looks like the "classical" AM waveform:
Ivan Akira under CC-BY-SA 3.0, source
In the frequency domain, the sidebands look like the following (original work). Notice how the original signal (at 6.7 kHz) was shifted up to the carrier1:
The receiver, tuned to 100 kHz, will detect signals at 100 kHz +/- some bandwidth. In the simplest case of double-sideband+transmitted carrier, this can be as simple as a crystal radio with a bandpass filter and rectifier.
More modern systems will often suppress either the upper or lower sideband, and may even suppress the carrier itself in order to be more efficient with their available bandwidth and power. For example, if the transmitter were upper sideband, suppressed carrier, it would have a more advanced mixer that would emit only 106.7 kHz in your example. In practice, the signal of interest has a richer spectrum2 than a single sine, and the mixer emits that same spectrum, shifted up into the upper sideband above 100 kHz.
Your receiver would need to have its own local oscillator running at 100 kHz3, and a mixer (i.e. a crystal radio style receiver would no longer work). It's receiving 106.7 kHz, and it's mixing it with its own 100 kHz tone. As we remember from earlier, the mixer emits a sum and difference of frequencies, so the receiver's mixer emits two signals: the 6.7 kHz signal sent by the transmitter, and a 206.7 kHz signal that we discard (e.g. with a lowpass filter).
two completely separate carrier waves (say 100KHz and 102KHz) transmitting the same 6.7KHz frequency would interfere.
They do interfere, but not for the reason you think. A station transmitting a 6.7 kHz tone using AM at a carrier of 100 kHz emits a sine at 106.7 kHz, which looks just like a signal of 4.7 kHz coming from the 102 kHz station. The sidebands of the two stations cannot safely overlap4, 5, so the two stations would have to use carriers with wider frequency separation.
The use of negative frequencies may be confusing here. For the purposes of this answer, they're nothing more than a mathematical formalism. However, if you dive deeper into the math behind single-sideband and modulation techniques other than AM, they become important.
If you're doing AM modulation of audio, it would be the audio spectrum. For digital systems, it would be the spectrum of some kind of modulation scheme, for example BPSK or QAM. It may also be from a system like OFDM that packs multiple simultaneous BPSK or QAM signals into one block of frequencies.
If the receiver's local oscillator is imprecise, the received signal may be garbled because it's being downconverted to the wrong frequency. Many practical radio systems (e.g. WiFi) include preambles that are very easy to decode and give the receiver an opportunity to get its local oscillator calibrated properly.
Some systems, like WiFi or 4G/5G, must cope with overlap. This is done in a few ways: Partial or brief interference (as well as simple noise) can be handled with error-correcting codes, and coordinated sharing of overlapping frequencies can be handled with a multiple-access protocol like CSMA or other multiple access protocols.
For certain radio systems, it's possible to share the same frequency by sending radio waves with different circular polarizations. This is the one instance where a reference to physical photon waves is necessary here.
If you do the math carefully, you'll find that certain types of modulation (e.g. FM, naive BPSK/QPSK/QAM with sharp switching) actually have frequency components up to an infinite bandwidth! However, the power of those faraway components is so feeble and miniscule that we can safely ignore it, and we talk about bandwidth in the sense of a range where we find most of the signal power. See, for example, Carson's Rule for FM systems.