Shalaamu y'all,
These two roots both have an equivalent meaning of "to write." But how they came to mean this is interesting to researchers, since actual writing of a language was not known to everyone in the post-Babel period (it had to be relearned after the many languages were created). The Semites were no exception.

The Hebrew root כתב 'kathav' means "to write" in Qal. Not much to it. There are two other attested conjugations in the Hebrew text: Piel 'kittev' is "to write evil," and Niphal 'nikhtav' "be written" and "to record."

'Safar' is a loanword from Akkadian šapārum (š = 'sh') meaning "to send (a message)," hence šiprum "(written) message" and šāpirum "writer" (where Hebrew gets the idea of writing). If this is so, 'safar' is not an original root in Hebrew.

We must try and break down the original meanings of these roots to its basic idea and how every one of these meanings were derived from the original foundation of the roots.

'Kathav' - In Arabic, the root kataba means "to sew together," therefore we get "to write" (literally "sewing letters together"), kitābun "book," and kutbatun "suture," i.e. something "sewn together" at the seams, and "gird." This is the only fully developed system of this verb in a Semitic language. Therefore the closest we can get to the Proto-Semitic is the meaning "to bind, tie, sew together," as original root meaning from which the others are derived, since a scroll is "sewn together" in segments, writing "binds" images together, and "gird" as being "tied" to around a person.

'Safar' - In Akkadian, it means "to send (a message or letter)." In Arabic, safara means "to go forth (on a journey)." 'Safar' was originally believed to have had the meaning "to scratch, scrape," which is probable, but not completely possible. The verb 'safar' meaning "to count" is now considered an early denominative from 'sefer' meaning "writing" or "book" (since numbers were scratched into a surface). Whatever the case, Akkadian and Arabic witness to an earlier Semitic meaning of "to send" for the root, hence a letter (or writing, even book, scroll, or tablet, if you will) being "sent" to another. Or even "to go forth" (as in Arabic), but with a causative literally meaning "to cause someone to go," i.e. "to send." Both are possibilities.

KTB = "to bind, sew together"
SFR = "to go forth" (causative "to send") or simply "to send"

Peace and blessings to you in your studies.
Shalaamu

~ Seitz Hal-Taw'am

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"You shall know the Truth, and the Truth shall make you free." -- John 8:32