What is the difference between "Page Break" and "New Page"?

If you use \newpage, the page will be directly "cut off" and a new one will begin. The text/paragraphs on the page will not be affected in any way. If you do this, you might have a lot of empty space on that page.

With \pagebreak, the paragraphs on the cut page will spread out over the page, so you will not have empty space at the bottom. The old page will not look like it is the end of a chapter.

Here is an example of the results of a \pagebreak and a \newpage (the pictures show the page on which the command was written):

They are similar, though they have a difference:

\newpage 

Forces the current page to end and starts a new one. This will pad the page with extra space at the end of the page.

\pagebreak [number]

Breaks the current page at the point it is located. Using the optional number argument changes this from a demand to a request with priority in a scale from 0 (low priority) to 4 (high priority). This will not put extra space at the bottom of the page.

See https://web.archive.org/web/20131716503200/http://help-csli.stanford.edu/tex/latex-pagebreaks.shtml for info on page breaking commands.