Grep not matching certain parts of man page - bash

Question

Grep doesn't seem to match certain strings from man output. It seems to be random in that I can't work out any rhyme or reason as to whether a string will match or not.
man sed | head -7:
SED(1) BSD General Commands Manual SED(1)
NAME
sed -- stream editor
SYNOPSIS
$ man sed | head -7 | grep sed # no match
$ man sed | head -7 | grep stream # match on "stream"
sed -- stream editor
$ man sed | head -7 | grep '\-\-' # match on "--"
sed -- stream editor
$ man sed | head -7 | grep NAME # no match
$ man sed | head -7 | grep SYNOPSIS # no match
This also happens when redirecting the output to a file and grepping that
$ man sed | head -7 > /tmp/sed.man
$ cat /tmp/sed.man | grep sed # no match
$ cat /tmp/sed.man | grep stream # match on "stream"
sed -- stream editor
$ grep sed /tmp/sed.man # no match
$ grep stream /tmp/sed.man # match on "stream"
sed -- stream editor
grep: grep (BSD grep) 2.5.1-FreeBSD
man: version 1.6c
macOS: 10.14.6 Beta
bash: GNU bash, version 5.0.7(1)-release (x86_64-apple-darwin18.5.0)
$ man sed | head -7 | hexdump -C
00000000 0a 53 45 44 28 31 29 20 20 20 20 20 20 20 20 20 |.SED(1) |
00000010 20 20 20 20 20 20 20 20 20 20 20 42 53 44 20 47 | BSD G|
00000020 65 6e 65 72 61 6c 20 43 6f 6d 6d 61 6e 64 73 20 |eneral Commands |
00000030 4d 61 6e 75 61 6c 20 20 20 20 20 20 20 20 20 20 |Manual |
00000040 20 20 20 20 20 20 20 20 20 53 45 44 28 31 29 0a | SED(1).|
00000050 0a 4e 08 4e 41 08 41 4d 08 4d 45 08 45 0a 20 20 |.N.NA.AM.ME.E. |
00000060 20 20 20 73 08 73 65 08 65 64 08 64 20 2d 2d 20 | s.se.ed.d -- |
00000070 73 74 72 65 61 6d 20 65 64 69 74 6f 72 0a 0a 53 |stream editor..S|
00000080 08 53 59 08 59 4e 08 4e 4f 08 4f 50 08 50 53 08 |.SY.YN.NO.OP.PS.|
00000090 53 49 08 49 53 08 53 0a |SI.IS.S.|
00000098
Googling is hard for this problem as any combination of "man" or "grep" doesn't mention my problem that strings (with no special characters) are not matching.

Answer 1

man-pages are using the roff-format (https://man.openbsd.org/roff). Do the following:
man sed > sed.man
vi sed.man
so you see:
SED(1) BSD General Commands Manual SED(1)
N^HNA^HAM^HME^HE
s^Hse^Hed^Hd -- stream editor
to convert a man-page to text without the ^H-stuff. have a look on http://www.schweikhardt.net/man_page_howto.html#q10
create a perl-Skript called strip-headers with the content:
#!/usr/bin/perl -wn
# make it slurp the whole file at once:
undef $/;
# delete first header:
s/^\n*.*\n+//;
# delete last footer:
s/\n+.*\n+$/\n/g;
# delete page breaks:
s/\n\n+[^ \t].*\n\n+(\S+).*\1\n\n+/\n/g;
# collapse two or more blank lines into a single one:
s/\n{3,}/\n\n/g;
# see what is left...
print;
change the rights on the perl-script chmod 750 strip-headers and run it with:
man sed | ./strip-headers | col -bx > sed.man
or
man sed | ./strip-headers | col -bx | head -7 | grep sed

Answer 2

macOS man doesn't support the --ascii flag, so I used col -bx to strip the annoying formatting from man for piping into other commands.
man sed | col -bx | grep SYNOPSIS
col -b: Do not output any backspaces, printing only the last character written to each column position.
col -x: Output multiple spaces instead of tabs.
Notes:
I've read that man is meant to detect whether you're piping to another command or into a file, etc, but that was not my experience. At least for man 1.6c, the default for macOS.
Solution using col: https://unix.stackexchange.com/a/15866
Thanks #Cyrus - I didn't know about hexdump
Thanks #Oliver Gaida - I didn't know cat and vi would show display differently