While working towards your business goals, the Interim CTO works on building the product in an efficient way, along with designing the whole engineering department. This includes selecting the right architecture, technology, tools, and infrastructure along with the team's ways of working, methodologies, processes, and roles and responsibilities.
The team responsible for inter-company processes, culture, and ways of working can have numerous names - Project Management Office (PMO), Delivery Board, Agile Coach, ... Interim Agile PMO would take exactly the task - define, describe, optimize and introduce your new ways of working - in a structured and agile way.
Engineering Manager is the leader of the technical / engineering team responsible for the software implementation. The Engineering manager leads and grows the engineering (development) team and takes responsibility for the team's (agile) processes and organization. Engineering Manager is also accountable for technology selection, implementation quality, development tools, and solution architecture.
Similar to "construction supervisors" Vendor Managers make sure you are receiving appropriate services from your software vendors and partners. In agile software delivery, the Vendor Managers are here to ensure that no efforts and budgets are wasted, processes are aligned, commitments are kept, and the quality of delivery is high.