You’re confusing the different definitions of “suffering”.
When Buddhists speak of transcending suffering, or eliminating suffering, or transforming suffering, what is meant by “suffering” is more accurately described (as Contrarini pointed out) as “dissatisfaction”, or “a sense of not-quite-right-ness”. This “dissatisfaction” is caused by “thirstful, selfish craving”. So, in short, the Buddhist goal is to transcend/eliminate/transform “selfish craving”. The transcendence/elimination/transformation of “selfish craving” leads to the “highest happiness” (or “nirvana”).
Christianity has a similar goal. (There is no need to say that the goal is “identical”, but at the very least, it is similar.) In Christianity, the goal is theosis, divinization, which is the partaking of the divine nature, commonly described as “heaven”. Heaven is a state/place in which no pain or death exists, no “suffering”, and no “dissatisfaction”. In addition, there is no “selfish craving” in heaven.
So, we see that Christianity and Buddhism have very similar goals: the end of suffering.
Now, the question becomes: how does one reach that goal/destination/culmination point?
In Christianity, one is to “take up one’s cross” and accept “suffering” for the sake of Christ. What this means is that one is to renounce one’s selfish lusts, hatreds, pride, envy, and other sinful tendencies. The renunciation of such sinful tendencies produces a type of “suffering”: giving up the sinful acts that you want to do, can produce a lot of discomfort and suffering!
In Buddhism, the realization of nirvana is done by “going upstream”, that is, going in the opposite direction of one’s selfish cravings for excessive sensuality, for domination over others, for comfortable ease. And when one goes against one’s “natural” tendencies of selfish craving, that produces a type of “suffering”: giving up selfishness produces a lot of discomfort and suffering!
In both Christianity and Buddhism, one type of suffering is needed (the suffering that
results from relinquishing selfishness or sin), in order to transcend/eliminate/transform the other, more basic type of suffering, the suffering that is
caused by selfishness or sin.
We can thus see that there are two types of suffering, for both Christians and Buddhists.
- The suffering that is caused by selfishness or sin. For instance, the selfish craving that produces drunkenness can result in suffering.
2 The suffering that is the
result of relinquishing selfishness or sin. An example of this would be the suffering that one feels when one decides to not eat that last, scrumptious piece of cake; or, the suffering one feels when one decides to follow a discipline for Lent.
In both Buddhism and Christianity, suffering #1 is the suffering that is not wanted. Suffering #2 is simply part of the package whenever you practice a real, spiritual discipline.
In either case, both sorts of suffering are finally ended in heaven, or nirvana.