I was doing a search here and came across this very interesting somewhat old post by friend @Martin. I will share my understanding.
Please note that sañña is not a mere “recognition” of an object; this mere recognition is precisely what phassa itself is. For, if one did not recognise an object, then no consciousness of it took place and therefore no contact was established. phassa is established only in so far as the object has been recognised, and there is no meaning in talking about any phassa otherwise, and regardless of whether this recognising, along with our subsequent emotional responses, where self-conscious or otherwise.
Sañña on the other hand is that which produces the impression, the emotive tone if you will, that is associated with the object being recognised, and it does that by recourse to memory. Picture a lion appearing in the horizon of the steppes; because the monkey has encountered a lion before, and since then learned that it is deadly dangerous, it has now recognised it again, and recognised its danger again; this is what sañña is, a fundamental force or function which will cause the monkey to scream and crane its nick to alert other monkeys of the approaching danger. Sañña here is the fearful impression which the appearance of the lion (eye-contact) gives rise to in the psyche of the monkey. Fear, then, and agitation, will be the corresponding vedana; and the desire to escape the tanha, and the running away the upadana.
This recognising again (emotional memory) is precisely what sañña is; a fundamental evolutionary adaptive mechanism that is necessary for learning and for survival, and for the regulation of emotion (vedana). In a certain sense, sañña is what makes vedana an intelligent, effective, and also adaptable utility. So picture now our monkey to be rather inexperienced; a toddler perhaps! Having screamed and craned its nick pointing with it at the approaching danger, it finds that no other monkey responds with fear! “What is the matter?!” It wonders, “why is no one running?! Last time a lion just like this caught one of us and tore it to shreds!” Then it takes a closer look now that the stimulating object has come even closer! Behold! This is no lion! This is just a stag!! The inexperienced monkey has confused them, because they have the same colour and size and both walk on four. Now all fear is gone, vedana has changed. But why? Because the impression, the emotive tone a deer evokes in a monkey’s psyche is one mostly of indifference rather than fearfulness (having learned in the past that a deer is not dangerous). Sañña changes, vedana changes, and so on. Without sañña there is no survival for the sentient organism: either it will fail in recognising a lion, and the danger of the lion, a second time it encounters it, or it will never learn how to distinguish between a lion and a deer, thus fearing both and escaping both (and everything else that resembles them), hence living in constant escape and avoidance and unable to access limited resources.
So much happens between phassa and vedana, only, it happens so fast that, without meditation, we can barely notice it. However we can actually discern sañña taking place in between, and not only that, but it actually directly fashions the subsequent vedana. You could say that sañña is a cognitive phenomenon, where vedana is the emotional-behavioural manifestation or experiencing of that phenomenon. This is so important! Learning, prejudice, and habits, are formed and reinforced through that process.
I liked your question a lot and I have often thought that sañña deserved a place in the paticcasamuppada just as it appears in the pañcupadanakhanda; it’s kinda puzzling that it is missing in the earlier!