C handles them transparently (usually with the ASCII code on nearly all not very ancient compilers).
Terminals handles the ASCII control code. As in the answer of @rici, on consoles usually they are equivalent, but terminals are a wide concept. \v
is used for printers (especially on old printers where one sent directly characters to printers [also now it is so, but sending Postscript code (also in ASCII), and never the old plain text + formatting sequences]), e.g. headers and footers. Also \f
makes a lot more sense on printer: new page.
The \v
and \f
are very seldom used. According The C Book (Annotated Reference), Table 866.2, \v
is used 0.31% of all escape sequences, and \f
0.44%.
BTW \f
(^L
) is more often found on C code (as ASCII character) then as escape character in C code. Some editors put it to split regions (e.g. for hiding/showing just some regions). But also this (in my experience) is fading out: editors are now smarter, so they could automatically select regions (functions, declarations, etc. levels, including also with any sort of documentation convention [in comments] just before declaration/definitions]).
Note: some escape sequences are also used on communication between programs, to define "end of record (but not of communication).