Before I delve into the boundaries between the two, I will first briefly define them:
Liberation theology centralizes around oppressed people freeing themselves. Scripture passages that highlight liberation of the poor and marginalized bolster this movement, namely the story of Jesus Christ as told in the gospels. Oscar Romero, James H. Cone, and Diana L. Hayes are among the most prominent names in liberation theology. South American and Black religious communities are the strongest proponents of liberation theology, interweaving womanism (black women prioritizing the equality of black women among both race and gender lines) and mujeristas (Latinas working to liberate both the poor and oppressed in their culture, as well as their culture overall against colonial influences).
Prosperity theology prioritizes the embracing of God-given gifts, namely material gifts. The idea is that God has given the faithful these gifts, and it would be ungrateful to give away those gifts - charity, according to prosperity theology, is against God's will. There are communities, though, who do emphasize giving in order to receive, but the giving is almost exclusively to leaders who are already wealthy. Joel Osteen is the most famous proponent, and he is in good company with Southern charismatic churches and other televangelists. Almost all of these are white, with almost no references to any of the gospels.
I am by no means the first person to connect the Trump administration and its supporters to prosperity theology (1, 2, 3, 4, 5, 6, 7, 8, 9). "Make America Great Again" has never included greatness for anyone who benefits from liberation theology - the declaration of making Mexico pay for a wall dividing the nation from the United States makes this clear, among many other points.
Although I may prioritize the liberation of oppressed people, especially in the face of the oncoming administration, it is not about me. After all, it is because of my platform as an able-bodied white person that I can put forward liberation theology with reasonable expectation of being received by other able-boded white people. It is up to me to use the benefits I systemically receive from prosperity theologians, now that they are coming into their greatest political power yet, to work towards this liberation while also understanding that it is from these systems, including my role in them, that oppressed people must be liberated. It is up to me to keep in mind these intersections while also understanding that I, no matter how hard I work, am not separate from the ivory tower that is prosperity theology.
Diana L. Hayes described it better than I could. In her connection between womanism and liberation theology, she said that it would be logically inconsistent for her to work with feminists (see: white) because it is from us (see: white) that she must be liberated.