There are many similarities between all forms of design, not just graphic and architectural design.
A term that summarizes how similar they are, Design Thinking, has even been used to describe how designers think and work. When you are designing anything, your brain works in a very distinctively different pattern then when you are being analytical or logical. Design thinking loops back on itself and refines over time, where other forms of thiking are more linear.
Design is also an iterative process, meaning you start with an initial idea and slowly refine in small increments over time.
All designers also use many of the same tools despite producing different results. I personally use photoshop, illustrator and indesign as much, if not more than I use CAD based software. Designers also generally use things like rulers, pens, paper, pencils, markers, and various other drawing supplies. Think kindergarten on steroids.
Design is also slightly different than art in such that design is a solution to a need, and art is an expression of an idea, feeling, messagage or more. This is not to say they are mutually exclusive. Art can be a design and design can be art.
Every designer is also constantly subject to their work being critiqued. Everyone has an opinion, and design is subjective. Every design is completely open to interpretation, and its success is determined by everyone but the designer.
Design disciplines field is rather wide – from transportation and urban design to interior design and not forget graphical, motion, or video game design. Nowadays any built-in environment is always produced with an interdisciplinary approach and deep specialization – in many cases needed special education and licensing. Sub-contractors cover their limited fields of responsibility (i.e. structure engineering, sometimes landscaping and transportation, electricity end many more). So architectural design can be described as a sub-discipline of a ‘big’ architecture, more focused on inner space (or you can say also urban interior), surfaces, furniture, materials, lighting fixture, sometimes navigation and advertising rules in public buildings (although this can be done by separate specialists on big projects like airport terminals), but no larger-scale functional division, building construction, etc.
Architectural design consultation could be considered an intellectual consulting firm that when retained, help the creative process of structural design while propagating cohesion with engineering limitations and protocol. *i.e. Help with the creative process and schematic procurement.
An architectural design Institution, if not a place to learn the trade, could be considered a construction arbitrator, for the literal facilitating of structure developments. *i.e. Manage vender and contractor services rendered.