In the Mahayana (great vehicle) and Vajryana (diamond vehicle) traditions the Bodhisattva looms large. In the “mythological scheme” the Bodhisattva remains in the cycle of life and death to continue to help others. The first of the 4 Bodhisattva vows is, “Sentient Beings are numberless; I vow to save them.”
The Buddha,in many places I've been, recedes a little into the background. In place of him you will find the Bodhisattva of Compassion, variously Avalokiteshvara, “He who hears the cries of all the world,” and Kuan Ying, or Kannon in Japan.
As far as I know, one doesn't hear much of Hindu missionaries. But Buddhism did spread, and on purpose. So there is a “missionary” side to it.
Buddhism is HUGELY various! In some traditions the Buddha definitely is presented as a savior who came to deliver us from bad karma. Now THAT’s a religion in competition with Christianity!
But in others while there is an agreed upon metaphysical starting point, which you can develop with scholastic intricacy, it's really all about the “practice,” about zazen. There are ethical precepts and they're considered in Buddhist communities. But the presentation is quite different from that in most Christian communities.
Counsellors, including pastoral counsellors, who don't have some kind of pshrink upstream are dangerous.
45 years ago I dropped out of seminary to do 15 months supervised work as a hospital chaplain with a “minor” in addictive disorders. I don't think I approached competence until 20 years ago.
And yes, there are a lot of wackadoodles studying psychiatry and psychology, in ministry, teaching, and everywhere. Thank God some of the wackadoodles at least try to help themselves and us.