\par is a TeX primitive and is the same as a blank line (except in special environments such as
verbatim where the usual rules don't apply). It ends horizontal mode, causes TeX to break the horizontal text into lines placed on the current vertical list, and exercises the page breaker which may possibly cause the next page to be shipped out.
\\ is different in almost every respect. It is a macro not a primitive, and its definition changes wildly in almost every LaTeX definition. The definition in normal text, a
center environment a
flushleft environment and a table are all different.
In normal running text when it forces a linebreak it is essentially a shorthand for
\newline this does not end horizontal mode or end the paragraph, it just inserts some glue and penalties at that point into the horizontal material so that when the paragraph does end a linebreak will occur at that point with the short line padded with white space.
You should rarely need to use
\\ in documents apart from its use in alignments (where it is a macro based on the
\cr primitive), and you should rarely need
\par in documents as a blank line should suffice.