"There's a saying that a hair dragged across your palm would feel like a hair across the eye for a buddha.
The idea is that with realization one is completely accepting of all experience. So something like burning your hand would be felt intensely. The pain is real enough. But with no attachment to self there's no panic; no sense of existential threat.
In the line you quoted, pain is referring to actual pain, such as toothaches, death of loved ones, lost wallets, etc. Suffering is referring to the self-clinging, existential anxiety associated with those things.
To some extent, anyone can experience the difference. For example, you develop a great pain in your body. Egoic mind begins to panic about the possibility that life could be cut short; plans might have to be cancelled... there's an existential threat to self. You're overwhelmed with ominous fear. Then you find out that the pain was caused by, say, a treatable abscess, and you're given antibiotics or whatever. Once you have the diagnosis and treatment, the pain hasn't actually changed, but now it's a mere sensation rather than an existential threat.
There is a semantics aspect. Pain and suffering are not technical terms in a Buddhist context. They can be interchangeable. So there's also the teaching of the truth of suffering. At the very least we suffer birth, old age, sickness and death -- even if we live the life of Reilly until 100 years old. That's part of the teaching on the 3 marks of existence: suffering, impermanence and egolessness. The point there is to present a common sense argument that pursuing worldly fulfillment is a losing proposition. No matter what, we suffer. Even trading your 100-room mansion and for an 80-room mansion is loss and suffering. Far worse suffering is not unusual. Impermanence highlights the fact that we can never hold onto anything. Even if you get all you want in life and buy lots of insurance policies, you could lose it, develop a debilitating disorder, etc. And of course, you could die at any minute. The third aspect of egolessness is explaining that we go through life trying to gain and maintain our ground; trying to be happy. We constantly try to confirm ourselves through reference to other. We buy property, pursue pleasures, try to avoid things we don't like, tell each other constantly who we are and what we think/feel... Yet there's a background sense of existential panic, because experience is ungraspable as a thing. Thus, self can never actually be confirmed. There's a nagging sense in the back of your mind that something very basic is very wrong. Like going onstage to give a talk and you can't remember whether you put your pants on, but you don't dare to look down and check. So we're always winging it. In the Buddhist teachings that's known as all pervasive pain. There's the pain of pain -- basic pain and loss. There's the pain of alternation -- the inability to ever hold on to happiness. And there's all pervasive pain. The first two are the primary worry of worldly people. The 3rd pain is often what brings people to the path. Most people are not even aware of existential angst. They're busy distracting themselves so they don't have to look down and check whether they have any pants on. But for someone on the path, all pervasive pain is generally the most obvious."
