(1983 - 1984)
The CL-360 is only an updated CL-40 but it marked an important change : while the original CL-40 had been made by Luxman in Osaka, the CL-360 was made by Alpine in Tokyo.
Both are tube preamps (three 12AX7 & five 12AU7 for the 360 ; same plus two 12BH7A for the 40), the 360 swapping the "DAD" input moniker for the more modern "CD". Both have SRPP circuit, NF type tone controls and STAR grounding circuit and separate windings and regulations for each block.
Some circuit changes occured inside : cleaner layout, change of transformer (round core for the 40 vs. smaller shielded EI for the 360), of the tone control circuit...
The beautiful wood enclosure of the CL-40 gave way to more economical sideburns, along a silly simplification of the "operation" LED design.
Yes, the CL-360 is a cheaper but more modern CL-40.
Bar an integrated amp "version" (LX-360, 1985) and a later A3040 LuxKit version of the 360, there seems to be only these two CL versions which isn't like the many many produced for the MQ-360 power amp partner...
The images on this page come from a german 1988 catalog (CL-360) and a japanese 1984 Luxman-Alpine/Luxman-Luxkit catalog (CL-40).
Until I can put my hands back on the detailed circuit descriptions and specifications of both versions, the basic specs for the 360 are already here below accessible.
A basic circuit description of the original CL-40 is available here ; a real CL-360 here ; a real CL-40 here.