If you are coming to typefounding and matrix making from a background in digital type, the first step is to un-learn nearly everything you were taught there. Due to a series of unfortunate events in the history of type and the computer, most of what is taught now as "typography" is simply wrong: a user cannot "kern" type, Helvetica is not a font, type has no baseline, type size is more basic than typeface design, leading is not interbaseline-spacing, and so forth. It's really rather astonishing how thoroughly wrong digital typographic terminology is. [1] It doesn't matter what you were taught, or who taught it to you, or what you want to believe. If you try to use these words in their "digital-typography" sense when making real type, you will fail because they do not describe reality. Metal is unyielding in this regard.
The best approach, really, is to get some actual metal type [2] and learn to set it and print from it. Alternatively, acquiring a linecasting machine such as a Linotype or Ludlow, or a composing typecaster such as a Monotype Composition Caster and Keyboard, and learning to use it will have the same illuminating effect. Short of that, it's necessary simply to learn what the words really mean.
The Vertical Alignment of Type
"Lining" is the act of establishing the vertical alignment of the printable face of a type on its body, typically not in isolation but rather in relation to other types. This leads to two distinct uses of the term: (1) "lining systems," which establish lining relationships between two or more (usually many) different types, and (2) "lining faces," which are series where different body sizes of the series line in simple integral point relationships with other sizes. Both of these are late 19th century innovations; for 400 years, type was vertically aligned only within a single size of a typeface.
The most difficult aspect of this for those trained digitally is the understanding that baseline is not a basic element of type.
The Horizontal Alignment and Width of Type
The horizontal specification of type consists of two things: (1) the set (aka set width) of the body of each type, and (2) the horizontal alignment of the printable face on the body of each type. Together these determine the horizontal "fit" of the resulting letterforms when printed together. Establishing them is termed "fitting."
While the lining of type since the late Victorian era typically involves at least an entire series and more typically many series, the fitting of type is done entirely within a single member of a series. Lining between more than one member of a series is an essentially modern proposition. It has been done systematically for only the last century and a half. Fitting is an ancient undertaking. It has been necessary for every type since Gutenberg.
See also kerns and mortising.
1. I had to learn the hard way myself. My history is in computer programming. Computers were the family business. My father started programming in 1958, and taught me to program in the 1970s. As with so many in my generation, Douglas Hofstadter ( Gödel, Escher, Bach) ruined my life (to my great delight) in 1980 by addicting me to both typography and formal systems theory. Thence to nroff and TeX (yes, I have all five volumes of Computers and Typesetting). I didn't actually handle real type until I was 46 years old, well into the 21st century. Since then I've had to unlearn fast.
2. Don't use wood type. You need to know how metal type is set in a composing stick. Because of its size, wood type is frequently set directly in a form on an imposing surface, or in some modern use straight on a proof press being used as if it were a production press. Trying to understand real type on this basis leads to things such as the illustration on p. 82 of Gregory Ruffa's The Art of Wood Type (Plainfield, NJ: GRA Publishing, 2008) which purports to show metal type being set in a composing stick but which actually shows metal type placed on its side in a composing stick, rotated 90 degrees from how it would actually be used. Type cannot be set this way. [TO DO - re-create the Ruffa photo]
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