Any answer to this depends on whether we are focusing on political or philosophical discourse, and whether we are using the terms as political labels or mere descriptors. Generally, in current discourse ‘Liberal’ is used as a political term whereas ‘idealist’ is more a philosophical term.
Liberalism is both a political movement and a philosophical alignment, but we typically use it as a political designation in modern Western discourse. So, a liberal is a person who follows the so-called left spectrum of the political continuum. A liberal usually believes in an active government that works for the benefit of the people.
An idealist is a person who believes in a certain set of ideals (understanding of what is perfect) and who tries to maintain strict adherence to those. Idealists are often perceived as unrealistic, or at least impractical, in that their ideals may not fit the actual reality of the world.
A liberal may indeed by an idealist, but liberals may also have a more utilitarian, practical focus. Further, a conservative (someone on the so-called right of the political continuum) may be an idealist in that he/she adheres to a set of ideals rather than focusing on more practical concerns. Thus, we see that an idealist in the philosophical sense is not someone of a particular political bent, but rather someone who puts his/her ideals before other considerations.
To complicate things, a person may be an idealist philosophically but not in practical application. For example, Thomas Jefferson’s writing show a strong idealistic bent, but his actual behavior, both in his personal life and his political life, frequently did not adhere to his expressed ideology.
In current political discourse, we often seem to use the term ‘idealist’ to mean someone, usually a liberal, who adheres to his/her political beliefs strictly and uncompromisingly. Further, ‘idealist’ as a political label is often conflated with ‘utopian’, and the term has even taken on a somewhat pejorative slant with respect to politics.