Yes, that is the carbine version.
Many Model 1865 Spencer carbines and rifles were purchased in 1866 by the pre-Confederation United Province of Upper and Lower Canada, or by the British War Department to be loaned (and later transferred outright) to the Canadian Militia Department, because of the Fenian Raids emergency (for more information on that little known aspect of Canadian military history, see
http://www.warmuseum.ca/cwm/exhibitions/chrono/1774fenian_e.shtml and
https://en.wikipedia.org/wiki/Fenian_raids). A total of 2,300 Spencer carbines and 2,000 Spencer rifles were brought into Canada. (Interestingly, that was about 2/3 of the total known production of the Model 1865 Spencer in the full-length rifle configuration!) Other breech-loading firearms were also acquired in the United States: 3,000 Peabody rifles and 1,000 Starr carbines. The purpose of these acquisitions was to re-arm, as much as possible, the Militia in Canada with breech-loaders rather than their standard .577 Enfield muzzle-loading rifles, for this emergency. Following the big raids in 1866, the threat of further raids remained a serious concern, but no more actual incursions actually took place until 1870. In the meantime, the Snider-Enfield rifle (conversion of the .577 Enfield to breech-loading) had been adopted, and 60,000 of them arrived in Canada in 1867, and the Militia were fully re-armed with Sniders by 1868, and the Spencers, Peabodies and Starrs were withdrawn from service.
The "cutoff" Colin mentioned is the "Stabler Cut-Off Device" invented by Edward M. Stabler in about 1864/65. It was a mechanism which could be installed in the Spencer action that, when activated, cut off the feeding of cartridges from the magazine tube in the butt, allowing the firearm to be used as a single-shot while keeping the cartridges in the magazine as a reserve. Apparently, the Spencer carbines and rifles brought into Canada for the Militia were
not fitted with this device, and it is accordingly one way of determining whether a particular Spencer is part of this "Canadian contract".
The selection lever for this device, if it has been installed, should be readily visible on the underside of the action just ahead of the trigger. I can't tell for sure, but in that side view you posted (of the whole carbine laying on the gun case) it appears that your carbine
may be fitted with the Stabler device ... can you give us a better view of that area? Here are some images showing the selection lever of a Stabler device:
First a side view, in which the selection lever can be seen ahead of the trigger -
Bottom views showing the lever in its two possible positions -
