Well, the answer typically depends on who is asked since there are many views and positioning of others.
Amongst the opinionated, we find the following roles or professions.
• Business executives, managers, and specialists
• Designers
• Business Designers
• Service Designers
• Business Architects (BA
• Enterprise Architects (EA)
⁃ System Architect, Solution Architect, IT architect. Data Architect, ...
• Building Architects
⁃ Architectural Designers
• Engineering Designers
Regarding Building Architects most agree on what they do, which is not surprising since the profession has thousands of years of practice to rely on. Also, building architects are primarily focused on creating artifacts and not so much on dynamic and VUCA socio-technical-economical organizations.
There are newcomers to the field, Business and Enterprise architects that work hard to position themselves in relation to others and also between themselves.
EA and BA often seem to position themselves as part of the business or strategic leadership teams although it seems as if business executives, in general, don't agree.
Business designers and agile practitioners often position BA and EA as a matter of technology as systems, which is what most EA seems to be concerned with.
One common view held by BA and EA is that they arrive before designers on the scene and designers do their work within the architecture. This is common in (IT) engineering processes.
However, when it comes to the design of the business, organizations, and products business executives seem to prefer business and (service) designers to be the primary responsible.
Maybe this is partially explained by the differences in toolboxes where BA and EA use assumptions closed and fixed frameworks in their job while designers use open-ended toolboxes suited to the challenges at hand.
Another area of dissonance is the common view held by BA and EA that architects work with 'abstractions', the 'what' and 'high level', and that designers work with the 'concrete', the 'how' and 'low level'.