Most authors prefer "length" for the anterior-to-posterior measurement
(just as you would measure the length of a snake or fish) and "height"
for the dorsal-to-ventral measurement.  Those who use this system (the
majority) generally use "width" for the lateral-to-lateral measurement,
but some use "thickness".  However, I have occasionally seen "width"
used instead of "length".  It is interesting the way these measurements
apply to shells of various families.  In general, we tend to describe
the size of a shell in terms of its greatest dimension, regardless of
which dimension that may be.  If you have a "2-inch Tellina", you are
speaking in terms of its length.  But a "2-inch Mytilus" is measured by
its height.  And a "2-inch Corculum" may refer to either the height or
the width, depending on the particular specimen, but never the length
which, in the flattened shells of that genus, is the shortest measurement.

Paul M.