In simple terms, "Science" is concerned with 'understanding fundamental laws of nature and the behavior of materials and living things'.

"Engineering" involves ‘the application of science and technology to create useful products and services for the whole community, within economic, environmental and resource constraints‘.

"Technology" is the application of scientific knowledge for practical purposes, especially in industry. Technology can be most broadly defined as the entities, both material and immaterial, created by the application of mental and physical effort in order to achieve some value. In this usage, technology refers to tools and machines that may be used to solve real-world problems.

On a more philosophical level, scientists tend to explore the natural world and discover new knowledge about the universe and how it works. Engineers apply that knowledge to solve practical problems, often with an eye toward optimizing cost, efficiency, or some other parameters.

For example a Scientists discover different ways to generate and use electricity. Engineers develop principles into practical components used to build power stations and enable the users of electricity to improve the quality of people’s lives.

A scientist may investigate the basic properties of various rock and soil types. An engineer uses this information to derive engineering properties that are needed to design structures (such as building foundations, retaining walls and tunnels) and to examine the stability of natural and man-made slopes (such as those in dams)

There is considerable overlap between science and engineering, so you will find scientists who design and construct equipment and engineers who make important scientific discoveries. Information theory was founded by Claude Shannon, a theoretical engineer. Peter Debye won the Nobel Prize in Chemistry with a degree in electrical engineering and a doctorate in physics.

Now lets dig into these two concepts in a bit more depth. Scientific inquiry expands the scope of human perception and understanding; engineering design expands the scope of human plans and results. Inquiry and design are perfectly distinct as concepts, but often interwoven in practice, whether within a field, a research program, a development team, or a single creative mind. Meshing design with inquiry can be as vital as hand-eye coordination.

"The essence of science is inquiry; the essence of engineering is design." - Eric Drexler

Engineering new instruments enables inquiry, while scientific inquiry can enable design. Chemical engineers investigate chemical systems, testing combinations of reactants, temperature, pressure, and time in search of conditions that maximize product yield; they may undertake inquiries every day, yet in the end their experiments support engineering design and analysis. But the close, interweaving links between scientific inquiry and engineering design can obscure how deeply they differ. Engineering new instruments enables inquiry, while scientific inquiry can enable design. Chemical engineers investigate chemical systems, testing combinations of reactants, temperature, pressure, and time in search of conditions that maximize product yield; they may undertake inquiries every day, yet in the end their experiments support engineering design and analysis. But the close, interweaving links between scientific inquiry and engineering design can obscure how deeply they differ.

Here is a schematic structure of Scientific inquiry contrasted with the structure of engineering design.

Scientific inquiry builds knowledge from bottom to top, from the ground of the physical world to the heights of well-tested theories, which is to say, to general, abstract models of how the world works. The resulting structure can be divided into three levels linked by two bridges.

At the ground level, we find physical things of interest to science, things like grasses and grazing herds on the African savannah, galaxies and gas clouds seen across cosmological time, and ordered electronic phases that emerge within a thousandth of a degree of absolute zero.

On the bridge to the level above, physical things become objects of study through human perception, extended by instruments like radio telescopes, magnetometers, and binoculars, yielding results to be recorded and shared, extending human knowledge. Observations bring information across the first bridge, from physical things to the realm of symbols and thought.

At this next level of information flow, scientists build concrete descriptions of what they observe.

On the bridge to the top level of this sketch of science, concrete descriptions drive the evolution of theories, first by suggesting ideas about how the world works, and then by enabling tests of those ideas through an intellectual form of natural selection. As theories compete for attention and use, the winning traits include simplicity, breadth, and precision, as well as the breadth and precision of observational tests— and how well theory and data agree, of course.

Thus, in scientific inquiry, knowledge flows from bottom to top.

At this level, the contrasts are often as concrete as the difference between a microscope in an academic laboratory and a milling machine on a factory floor. At the higher more abstract levels of science and engineering, the differences are less concrete, yet at least as profound. Here, the contrasts are between designs and theories, intangible yet different products of the mind.

Scientists seek unique, correct theories, and if several theories seem plausible, all but one must be wrong, while engineers seek options for working designs, and if several options will work, success is assured.

Scientists seek theories that apply across the widest possible range (the Standard Model applies to everything), while engineers seek concepts well-suited to particular domains (liquid-cooled nozzles for engines in liquid-fueled rockets).

Scientists seek theories that make precise, hence brittle predictions (like Newton’s), while engineers seek designs that provide a robust margin of safety.

Scientific inquiry faces toward the unknown, and this shapes the structure of scientific thought; although scientists apply established knowledge, the purpose of science demands that they look beyond it.

Engineering design, by contrast, shuns the unknown. In their work, engineers seek established knowledge and apply it in hopes of avoiding surprises. In engineering, the fewer experiments, the better.

Inquiry and design call for different patterns of thought, patterns that can clash. In considering the science in the area around an engineering problem, a scientist may see endless unknowns and assume that scarce knowledge will preclude engineering, while an engineer considering the very same problem and body of knowledge may find ample knowledge to do the job.

Engineers think that equations approximate the real world.
Scientists think that the real world approximates equations.
Mathematicians are unable to make the connection.
- Unknown (Humor)