The electromagnetic field around the antenna is the sum of all the waves (at all frequencies) in the vicinity. There is just one varying voltage at the output of the antenna. The RF stage of the receiver filters our all frequencies but those in the wanted channel. The detector (if we're talking about AM signals, this will just output the 'envelope' of the modulated signal) just detects the sum of the two signals which have been selected (i.e. just one varying voltage). When there is a big difference in amplitude, it will give you the envelope of the larger with extra garbage due to the interfering signal. You very often get a strong 'beat'. When the signals are nearly equal in amplitude, the beat is very strong and the wanted programme is inaudible - but what you hear is the sum of the two programmes plus this beat.
For FM signals, the situation is more complicated. After the RF filtering, the fm discriminator (not a simple detector) will give a signal which is proportional to the frequency of the stronger signal with a small amount of the weaker, due to the phase perturbation caused by the other RF signal. For wide deviation signals (fm broadcast), the carrier frequency sweeps over a large range and the interfering signal is 'drowned' by the larger one (the so-called Capture Effect) and so is the noise in the channel (often called the FM advantage over AM). When interference or noise are below a certain level, the demodulated signal is vey good because the frequency information is very robust but, past a certain 'threshold' level of noise or interference, the discriminator can no longer be 'sure' of the frequency it is looking at and you can get enormous noise spikes and the interfering signal can capture the receiver.
So, within the 'service area', you get pretty uniformly good reception but, outside it, the signal can be pretty useless and you will suddenly 'switch' to the other signal.
In your post, you use the word "mix". This, strictly, is what happens when there is a such a strong signal in a nearby channel that the non-linearities in the receiver generate 'artifacts' such as cross modulation. When this happens, the stronger signal, although at a different frequency, can produce frequency products that are audible. It is counter-intuitive but you can sometimes reduce the effect of a strong interferer by reducing the input of RF signal to the set as it reduces the effects of the non-linearity.