There are several ways to write commands with multiple lines in Dockerfile, for example you wanna echo a bash file entrypoint.sh with content:

#!/bin/bash
echo 3
echo 2
echo 1
echo run

You could:

Using printf

RUN printf '#!/bin/bash\necho 3\necho 2\necho 1\necho run' > /entrypoint.sh

Using cat

RUN sh -c "$(/bin/echo -e "cat > /entrypoint.sh <<EOF\
\n#!/bin/bash\
\necho 3\
\necho 2\
\necho 1\
\necho run\
\nEOF\n")"

Using echo -e

RUN echo -e " #!/bin/bash\n\
echo 3\n\
echo 2\n\
echo 1\n\
echo run" > /entrypoint.sh

Using $'...'

The $’…’ feature is known as "ANSI-C quoting" but it’s not a POSIX shell > feature. According to unix.stackexchange.com/a/371873/109111 it was > originally a ksh93 feature but it is now available in bash, zsh, mksh, > FreeBSD sh and in busybox’s ash

RUN echo $'#!/bin/bash\n\
echo 3\n\
echo 2\n\
echo 1\n\
echo run' > /entrypoint.sh

echo -e & $'...' are both similar in that they support the following escape sequences:

\a     alert (bell)
\b     backspace
\e
\E     an escape character
\f     form feed
\n     new line
\r     carriage return
\t     horizontal tab
\v     vertical tab
\\     backslash
\0nnn  the eight-bit character whose value is the octal value nnn (zero to three octal digits)
\xHH   the eight-bit character whose value is the hexadecimal value HH (one or two hex digits)
\uHHHH the Unicode (ISO/IEC 10646) character whose value is the hexadecimal value HHHH (one to four hex digits)
\UHHHHHHHH
     the Unicode (ISO/IEC 10646) character whose value is the hexadecimal value HHHHHHHH (one to eight hex digits)

They do have differences. In addition to the above, echo -e supports:

\c     suppress further output
\0nnn  the eight-bit character whose value is the octal value nnn (zero to three octal digits)

By contrast, $'....' supports:

 \'     single quote
 \"     double quote
 \nnn   the eight-bit character whose value is the octal value nnn (one to three digits)
 \cx    a control-x character