We are taught not to use the word "pain" because it has been shown to sensitise people, resulting in them experiencing worse pain than they otherwise would.
There is also a difference between pain caused by HCP (injections, local anaesthetic infiltration, post operative pain) vs pain caused by whatever condition the patient is suffering from.
Our recovery nurses are taught not to ask if the patient is in pain, but if they are comfortable. If they use the word "pain", most patients say yes. However, if you ask if they are comfortable, also most patients say yes. So which ones do you give pain relief to? For that you have to be guided by the physiological signs (heart rate, blood pressure, resp rate) and the patient themselves. We tend to ask if the patient is comfortable first and if not (or if they are obviously not), only then ask them to rate their pain out of 10. If someone is fast asleep, opens their eyes and says '10' and then falls asleep again, they are unlikely to be given much in the way of pain relief. If someone is wide awake and says 'it's about a 5-6' then they'll be given something to bring it down to below a 4.
If I tell someone that something is going to cause pain, they tense up and the pain caused is of greater magnitude than if I tell them they are going to feel a stinging sensation or a sharp pinch.
As far as non-procedural pain goes - yes by all means use the word pain, but we need it clarified and quantified. Burning, stinging, aching, hot/cold, radiating, dull/sharp, constant or coming and going - not all pain responds to traditional painkillers and some types of pain need a different approach.
And yes, some patients lie. I find it easier to assume that they are all telling the truth to begin with and only modify my management if it's obviously needed.