Otdfbt

What means the following extract on page 46 of TeXbook?

TeX goes into state S in case (c), or in case (b) with respect to a character of category 10 (space)

Does it mean that space must be skipped in case (b)? If yes, why the following example shows contrary?

chardefx=`%

% a % case (b) - not skipped

x a % case (c) - skipped

bye

Also, does the "with respect to a character of category 10 (space)" part relate to "case (b)" only, or to both?

This is the full paragraph:

If TeX sees an escape character (category 0) in any state, it scans the entire
control sequence name as follows. (a) If there are no more characters in the
line, the name is empty (like csnameendcsname). Otherwise (b) if the next character
is not of category 11 (letter), the name consists of that single symbol. Otherwise (c) the
name consists of all letters beginning with the current one and ending just before the
first nonletter, or at the end of the line. This name becomes a control sequence token.
TeX goes into state S in case (c), or in case (b) with respect to a character of category 10
(space); otherwise TeX goes into state M.

For a different perspective: the paragraph is an attempt to explain section 354 of the TeX program, and the part about the state is the blue rectangle below (the included sections 356 and 355 happen not to affect state):

So what it means is that if the character immediately after the escape character is either a letter, or a space [this is what is written in the TeXbook as “case (c)” and as “case (b) with respect to a character of category 10 (space)” respectively], then TeX goes into the skip_blanks state, else it goes into the mid_line state.

Because of the tangled evolutionary history of TeX and The TeXbook (my understanding is that first TeX was written, then a manual was written explaining it, then TeX was completely rewritten in such a way that the manual didn't change much(!), then the manual continued to be tweaked to account for tweaks to TeX), it can sometimes be easier (IMO) to understand some aspect of TeX by just reading the code than to read the TeXbook.

Appendix: If you find the image hard to read, here is the section again, taking the code from tex.web and reformatting it a little and putting the labels in uppercase:

 @<Scan a control...@>=
 begin
 if loc > limit then
 cur_cs := null_cs state
 else
 begin
START_CS:
 k := loc;
 cur_chr := buffer[k];
 cat := cat_code(cur_chr);
 incr(k);
 if cat = letter then
 state := skip_blanks
 else if cat = spacer then
 state := skip_blanks
 else
 state := mid_line;
 if (cat = letter) and (k <= limit) then
 @<Scan ahead in the buffer until finding a nonletter; if an expanded code is encountered, reduce it and |goto START_CS|; otherwise if a multiletter control sequence is found, adjust |cur_cs| and |loc|, and |goto FOUND|@>
 else
 @<If an expanded code is present, reduce it and |goto START_CS|@>;
 cur_cs := single_base + buffer[loc];
 incr(loc);
 end;
FOUND:
 cur_cmd := eq_type(cur_cs); cur_chr := equiv(cur_cs);
 if cur_cmd >= outer_call then
 check_outer_validity;
 end

in case (c), or in case (b) with respect to a character of category 10 (space);

means the cases that the character after is a letter (case c) or the character after is a space (case b (non-letter) in the case that it is a space)

So in those cases the following space is skipped,

In other cases (non-letter, non-space) then the space is not skipped.

So, a <space> acts as case b (non letter) in that only one character is considered part of the name, but it acts like case c (letter) in that following spaces are skipped.