I can find lots of answers about what the differences are between these, or what they are functionally, but I want to know if there's a name for characters like these that typically don't show up as a character so much as they change the structure and placement of other characters.
I've seen "control character", I've also seen "character sequence". I'm not sure what's correct, or if there is a correct term.
All of them are whitespace characters which are intended to move the print head on a terminal. They're also part of a larger set of control characters which are intended to communicate with a print terminal rather than be printed directly. (ASCII was based on earlier systems that managed teletypes, not computer displays.)
"Character sequence" is just a sequence of any characters, so that would be even more general.
The specific syntax of a leading backslash and a character to indicate some other unprintable character is called an escape sequence, and specifically a C-style escape sequence.
"Whitespace" is the general term for space/tab/newline/etc.
In "regular expressions", \s and/or [[:space:]] represents a single whitespace character.
Not quite what you asked, but...
There are other characters that neither show nor take space. See "non-breaking hyphen" and "soft hyphen".
Also, there is a class called "nonspacing marks". Example: An accent mark that displays above the subsequent letter.
