A path tracer is a Monte Carlo ray tracer (not all ray tracers are path tracers, but all path tracers are ray tracers). Arnold can be configured with sample settings such that it gets very close to being a pure path tracer, but typically it allows "splitting" where after an intersection, at a given ray intersection the path can split and have two branches or sub-paths.
If you set the sample settings such as GI_diffuse_samples or GI_specular_samples to be greater than one, Arnold will split paths at the first hit. After that, it will forego splitting as much as possible, however it is still acting as a general Monte Carlo ray tracer.
Due to motion blur and depth of field, it is common for production scenes to need higher AA_samples to resolve that type of noise, and users usually set all or nearly all of the other sample settings set to 1 each. This puts Arnold in a mode that is very close to pure path tracing.
So the answer, in the end, is that Arnold is both.
