I'm a shader dev working on a path tracing shader (Continuum RT), and you have no idea what you're talking about.

Raytracing is a family of lighting algorithms that use raycasting (using rays to find objects in the scene) to compute lighting within a scene. Multiple different algorithms exist within that family, and they're all considered raytracers.

Path tracing is a particular kind of raytracing which involves bouncing rays around in a random distribution, to eventually converge on a final unbiased result.

Number of rays doesn't matter, you could send a ray for every type of interaction (diffuse, specular, transmission/refraction), and so long as your ray distribution is random (rays are being cast in random directions), it's considered pure, unbiased path tracing.

Given an adequate amount of samples (we're talking potentially millions), unbiased path tracing is literally the most accurate type of lighting algorithm in computer graphics. It's so accurate, that it's often used as the ground truth method (will an utterly ridiculous amount of samples to ensure there's no statistical error present) to compare against other lighting algorithms.

It isn't the only type of raytracing, there are others, but among them all, path tracing is considered to be the most accurate, by the entire industry. Go ahead and read it up, I'll wait.