From my perspective:
Building Engineering consists of overall design needs. Working under an architectural firm, to produce a design of structural, mechanical, electrical etc. that will meet various code, cost constraints. Producing construction documents such as plans and specifications.
Building technology consists more of hands on installation and construction management.
Building trade technicians, follow design documents procuring and installing materials and equipment to deliver building systems that meet desired customer end results.
If a more detailed answer is required, probe with search engine. Getting a building from conception to finished product is complicated, typically does not conform to assembly line/repetitive approach.
