diamond cuts : ideal, perfect, hearts & arrows - what's the difference

I am doing some research before getting a diamond ring for engagement.
Many commented than cuts is the most important of the 4Cs. For various
websites & newsgroup, people are using the terms such as ideal cut,
perfect cut and hearts & arrow symmetry.

I wish to find out if there is a distinction between ideal cut and
perfect cut. Do they mean the same thing? Also, if we say that a
diamond displays hearts & arrows, do we mean that it is an ideal cut
diamond?

Thanks in advance.