What is the difference between a engineer and a architecture?

An architect is responsible for managing overall design of a building used primarily by persons, with primary emphasis on space planning and appearance. The architect should know enough about engineering to be able to discuss and understand the problems and solutions involved in engineering. For the type of building projects where an architect is required, engineers will tend to work for the architect.

An architect is not an engineer. Architects providing services to the public must be licensed by the governing authority (a state in US).

In general, engineering involves the application of scientific principles to solve practical problems.

An engineer is not a scientist.

A "professional engineer" ("PE") is licensed by the governing authority (a state in the US) to practice engineering.

Engineers use mathematics much more than architects. Some engineers use higher mathematics constantly. Engineers also tend to use software much more than architects, althogh architects use CAD programs extensively.