An architect is a licensed professional who has passed the registration exam - a very rigorous seven-part exam that is administered by the NCARB (National Council of Architectural Registration Boards). This exam is to architects what a bar exam is to lawyers.
An architectural designer is not a licensed architect, and has not passed the registration exam.
Note: an architectural designer should not be confused with a design architect, who has passed the registration exam and is a licensed architect, but chooses to only deal with the design aspect of a project, and lets another architect deal with the construction end of things.
A neurologist is a medical doctor who specializes in treating diseases that affect the human nervous system.