CL2 and CL3 cables are both meant for indoor in-wall use. (See last paragraph below.) I'm not sure if they meet code for outdoor use. When you say "outside under your deck", do you mean suspended above ground, or buried underground? You'll have to check your local building and electrical codes to be certain.
To directly answer your question, I think splicing CL2 and CL3 would be OK as long as it's domestic use and not commercial. But you may have to do something else, such as use a water-proof outdoor conduit, to use that in-wall wire outdoors.
CL2 and CL3 cables are coated with insulation and jacket material that releases less toxic gas if the cable catches on fire. CL2 cables are certified to carry up to 150 volts and are designed for residential uses, while CL3 wires can handle 300 volts and are intended for use in commercial settings.