The term "pen and paper" can practically be interpreted as "using no tools like electronic devices", since it targets cryptographic functions, schemes, and procedures which can be handled by humans who have nothing more available than the option to use manual writing. So, "pen and paper" can also mean "pencil and post-it", "chalkboard and chalk", "wall and spraycan", etc. Mental calculations and reasoning processes are also included.
The term "pen and paper" refers to cryptographic functions, schemes, and procedures that can be handled by humans, without access to computers or other electronic equipment. So, "pen and paper" can also mean "pencil and post-it", "chalkboard and chalk", "wall and spraycan", etc. Purely mental schemes are less common but would require similar complexity and techniques, so they are included for practical reasons.
To explain it a bit more practically: the term "pen and paper" originates in military cryptography, where soldiers in the field can frequently find themselves in situations where they need to apply cryptography to transport messages in a secure way, but have nothing but a pencil and some paper available to do so.
On the Cryptography stackexchange, the more specific classical-cipher tag applies to cryptography that historically existed before computers, while the more general "pen-and-paper" tag also applies to recently-created cryptography.
The related lightweight tag can be seen as covering cryptographic systems intended to run on slow, low-memory smartcards and other constrained systems, rather than general-purpose computers.
