How do terms such as 'Left' and 'Right' relate to 'Liberal' and 'Conservative'?

A brief attempt to define some terms common in current political discourse.  Terms such as left and right are often correlated with, and very commonly substituted for terms such as liberal and conservative.  This happens in a way that often renders any subsequent discussion confusing and muddled.  Below are some provisional definitions, or better, descriptions intended to help clarify at least some of what I will likely say in the future.

Right:

-Religious: seeing religion as a stabilizing force.

-Puritan: isolational, seeing culture as an integrated whole, it should be stable, fixed, unchanging, traditional.

-Dichotomic: seeing the world in terms of clearly defined, often oppositional structures. Valuing clarity.

-Metaphysical: seeing non-physical (i.e., cultural, psychological, aesthetic), mental qualities as real and external, i.e., “in the external, physical world.”

-Litigious: seeing the law as an acceptable means not just for social, but for cultural and aesthetic control.

-Hierarchic: seeing hierarchies as real, and so as important and desirable structures, and elites as trustworthy models of ethical value.

Left:

-Areligious or even anti religious: seeing religion as a means of elite cultural control. Spiritual concepts when in place, are less well defined.

-Integrational and appropriative: seeing cultural forms as modular, and so cultural states as provisional and adaptable.

-Gradaional: seeing the world in terms of poorly defined structures better represented as spectra of possibilities. Valuing nuance.

-Materialist: non-physical aspects of life are constructs and idiosyncratic.

-Activist: seeing the law as a tool of elite control.

-Egalitarian: seeing hierarchies as oppressive, elites as untrustworthy, because they allow themselves to invent or abrogate ethical standards.

Conservative: change and difference are disruptive and potentially socially harmful; stability and tradition are idealized; a tree needs strong roots.

Liberal: change is unavoidable and often desirable; tradition is often stifling and favors elites; a shark must keep moving or die.

Note how the terms left and right defined here reflect a cluster of features. A prediction arising from this, is that not all individuals who identify as left or right  or who are so defined by others, will necessarily express all of the relevant features.  And this appears to be born out.

The two sets of oppositions, left/right and conservative/liberal as defined above seem to differ in an important general way, such that we can consider the conservative/liberal spectrum as a basically quantitative one, since it seems to relate to the degree to which change is valued, whereas the left/right spectrum, involving a number of parallel qualities, can be viewed as a qualitative spectrum.  A prediction arising from the definitions above is that we should be able to correlate the two spectra in such a way as to expect the possibility of finding individuals who identify as conservative leftists as well as conservative rightists, and liberal rightists as well as liberal leftists.  However, based on the above descriptions, we can see how the correlation and often the confusion between conservative and right, as well as liberal and left arises.  But it arises, not because of the two sets of ideas (left/liberal, right/conservative) are synonymous, but because they share important features.  Defining these terms as above (vel sim.) allows our discussion of these important positions to proceed without becoming hopelessly muddled and confused.