There are three kinds of suffering:
(1) Suffering of suffering (or ordinary suffering),
(2) Suffering of change (or suffering caused by changes), and
(3) All-pervasive suffering.
The first suffering is what we usually call suffering. It is the experience we feel when we have a specific problem, like being sick, losing money, or feeling the pain of the death of a close person.
The second kind of suffering is produced by so-called happy experiences, which then bring about unhappy results due to the impermanence of samsāric phenomena. For example, although we are enjoying eating good food, the enjoyment might change into the pain of digesting it. Similarly, today we are enjoying earning a lot of money, but it might cause us to worry about protecting, preserving, or investing it. Someone could be excited today with his or her lover, but one day might be in pain because of separation.
Third, all compounded things are subject to change and decay, and they are all created by the cause of suffering—dualistic concepts and emotional afflictions.
So there is nothing in the world that is not permeated by suffering.
(Source: Thondup, Tulku. Enlightened Journey: Buddhist Practice as Daily Life. Shambhala. Kindle Edition.)
More Detailed Description
The Buddha distinguishes three kinds of suffering:
(1) Visible suffering,
(2) The suffering of change, and
(3) The universal suffering that is inherent in all phenomena composed of elements that come together momentarily and are transient by nature.
Visible suffering is evident everywhere: illness, death, war, natural disasters, and so forth.
The suffering of change is the suffering latent in the various pleasures that seem to last but sooner or later turn into their opposites. The fleeting experience of pleasure is dependent upon circumstance, on a specific location or moment in time. It is unstable by nature, and the sensation it evokes soon becomes neutral or even unpleasant. Likewise, when repeated, it may grow insipid or even lead to disgust; savoring a delicious meal is a source of genuine pleasure, but we are indifferent to it once we’ve had our fill and would sicken of it if we were to continue eating. Pleasure is exhausted by usage, like a candle consuming itself. It is almost always linked to an activity and naturally leads to lassitude by dint of being repeated. Listening to beautiful music requires a focus of attention that, minimal as it is, cannot be maintained indefinitely. Were we forced to listen for days on end, it would become unbearable. This type of pain can occur at any moment of our lives, but we never think of it that way. We are fascinated by the mirage of appearances and forget that beings and things are constantly changing.
Finally, universal suffering is the most difficult to detect because it is concomitant with the blindness of our mind and is constantly renewing itself as long as we are in the grip of ignorance and attachment to the ego. It stems from the fact that we have not grasped what we need to do to avoid suffering. This confusion and the tendencies associated with it lead us to perpetuate the very actions that are at the root of our troubles. To dispel this suffering, it is necessary to wake up from the sleep of ignorance and understand the mechanisms of happiness and suffering.
(Source: Ricard, Matthieu. On the Path to Enlightenment: Heart Advice from the Great Tibetan Masters. Shambhala. Kindle Edition.)