The log held by the University of Pennsylvania is entitled an "abstract log", implying that it was a digest of the main master's navigational log. It also contains an appendix devoted to the cyclone of 1864, wherein Joseph Watson copied both a letter detailing what he witnessed (sent to an Indian newspaper) and other newspaper accounts.
What we find for the Clarence at the Maritime History Archive in St John's are official logs
maintained in accordance with the Merchant Shipping Act of 1850 - legally required documents detailing the crew and their conduct, discipline and births and deaths aboard ship. Such logs were required to be submitted upon arrival in the final port of call. (Among the logs at the MHA, one occasionally finds notes of reprimand appended to the logs when masters failed to record required information.)
A. R. T. Jonkers. "Logs and Ship’s Journals." The Oxford Encyclopedia of Maritime History
. : Oxford University Press, 2007. Oxford Reference
. 2007. Date Accessed 10 Dec. 2015 <http://www.oxfordreference.com/view/10.1093/acref/9780195130751.001.0001/acref-9780195130751-e-0484>.