Opioids aren’t pure mu-agonists, they also have sigma agonists effects which produce non-opioid effects and also have off effects (histamine release). Combine that with the onset and duration of action, users can definitely tell if they got fentanyl versus say morphine. But not really between heroin and morphine.
As neuropharmacology and biology remain fields of active investigation, there are several other putative opioid receptors which aren't characterized very well at all but probably have some relevance. Diverse multiple-receptor heteromers are beginning to demonstrate pharmacological relevance (e.g. different binding profiles at mu-delta heteromers) and also at other protein-protein interaction sites (e.g. some drugs inhibit arrestin recruitment and activity dependent receptor internalization).
Also the pharmacokinetics/dynamics matter, things like the central/peripheral availability (e.g. how much constipation) and speed of availability to CNS. Metabolites may be psychoactive or may affect metabolism of the primary drug.
Off-target activity is present in everything and may be meaningful especially in some analogues (e.g. pethidine has significant dopamine transporter inhibiton) or in plant-derived morphine/heroin which comprise a complex mixture of compounds with diverse activities).
All of these things color the subjective experience of a drug. There is not much study made of subjective qualia because the models to describe this sort of thing are not very nuanced or descriptive, but more because it is not very relevant to clinical clinical practice. However, people who use tons of these drugs all the time do report subjective differences along dimensions such as "speediness", sedation, euphoria, "rushiness", malaise, therapeutic index, timecourse, etc. For example a user might report "Compared to heroin, oxycodone feels more energetic, while fentanyl has a nice initial rush but is much more sedating and wears off quicker", stuff like that.
TL;DR in vitro mu-opioid activity is not sufficient to explain objective or subjective variance between opioid drugs, and like much other biology there is much work to be done for all the nuance to be well understood.
https://en.wikipedia.org/wiki/Endorphins
> "Endorphins are released from the pituitary gland, typically in response to pain, and can act in both the central nervous system (CNS) and the peripheral nervous system (PNS). In the PNS, β-endorphin is the primary endorphin released from the pituitary gland. Endorphins inhibit transmission of pain signals by binding μ-receptors of peripheral nerves, which block their release of neurotransmitter substance P. The mechanism in the CNS is similar but works by blocking a different neurotransmitter: gamma-aminobutyric acid (GABA). In turn, inhibition of GABA increases the production and release of dopamine, a neurotransmitter associated with reward learning."
All that matters is that the drug molecule binds to the receptor proteins in the brain and peripheral nerves. Studies show that the active dose is directly related to the binding strength of that specific molecule (fentanyl binds more strongly than heroin, so less is needed to get the same effect, oxycontin is about as strong a binder as heroin, about twice as potent as morphine).
Overdose deaths are generally due to (1) unusually high concentrations of active substances or (2) Users who've lost tolerance for some reason taking too much.
Legalization would likely eliminate most accidental overdose deaths as products would be clearly labeled as to contents.