What you're seeing is just ordinary text character set conversion.
As far as PuTTY is concerned, you are typing (and reading) text, not raw binary data, therefore it has to convert the text to bytes in whatever configured character set before sending it over the wire.
In other words, when you type Alt+1 8 2, PuTTY receives the corresponding character from the legacy "OEM" charset that the system is configured for. (Typing Alt+0 1 8 2 would choose from the legacy "ANSI" (Windows-125x) character set.) In this case, the character is
¶, a pilcrow.
Now PuTTY has to convert that character to bytes. Earlier PuTTY versions by default would choose the same legacy Windows-125x character set as the OS itself uses, e.g. Windows-1257, so the conversion used to be almost direct – input 1 8 2, receive byte 182 decimal (0xB6 hex).
However, as PuTTY usually connects to Linux or BSD servers, the huge majority of which have migrated to UTF-8 as the default, the latest PuTTY release started using UTF-8 by default as well. UTF-8 is an encoding of the Unicode mega-character-set, which has
¶ at position U+00B6, and it is mostly just coincidence that UTF-8 encodes that value as bytes
0000|0000 10|110110 →
00010 110110 →
0000|0000 11|111100 →
00011 111100 →
0010|0000 10|101100 →
0010 000010 101100 →
E2 82 AC
Wikipedia has it with colors
As a different example, the letter
ė used to be byte
E6 in the Windows-1257 charset, but in Unicode it is U+0117, corresponding to bytes
C4 97 in UTF-8. These sequences are of variable length, up to 4 bytes for larger positions.
If you absolutely must use PuTTY to send binary data, open the "Window → Translation" settings screen, and choose either CP437, ISO-8859-1, or Windows-1252 as the "Remote character set". (Save this in a separate session; do not save this as a global default because it will break regular SSH connections.)