Hfrhyu

The sed, which comes with FreeBSD 11.2 p7, gives:

 $ seq 10 | sed 'N; l; D; p'
1$
2$
2$
3$
3$
4$
4$
5$
5$
6$
6$
7$
7$
8$
8$
9$
9$
10$

While gsed (GNU sed 4.7) gives for the same script:

$ seq 10 | gsed 'N; l; D; p'
1n2$
2n3$
3n4$
4n5$
5n6$
6n7$
7n8$
8n9$
9n10$
10

How can we explain this difference in behavior?

BSD sed, when using l to output characters in a visually unambiguous form, does not output newlines in a visually unambiguous form.

From sed(1) on OpenBSD:

 [2addr]l
 (The letter ell.) Write the pattern space to the standard output
 in a visually unambiguous form. This form is as follows:

 backslash \
 alert a
 backspace b
 form-feed f
 carriage-return r
 tab t
 vertical tab v

(note lack of mentioning of newlines).

GNU sed, however, includes newlines in the set of characters to display unambiguously. It does this as an extension to the set of characters that the POSIX standard for sed mentions (which is the set that BSD sed uses). GNU sed behaves this way even if --posix is used on the command line.

GNU sed also outputs 10 twice, while BSD sed does not. Running GNU sed with POSIXLY_CORRECT set or with --posix will make it output 10 only once, like BSD sed does.

This is because GNU sed by default ignores the part of POSIX definition of the sed N command that says

If no next line of input is available, the N command verb shall branch to the end of the script and quit without starting a new cycle or copying the pattern space to standard output.

Note also that the p in your sed program never executes, as D starts a new cycle.