"Design" is a word which seems to be used differently by distinct groups of people. In software engineering, the word has an almost neutral meaning - something along the lines of "the way how the bits and pieces are put together", recognizing that there are many such ways and that they may be told apart based on some definable characteristics. Of course, there is also talk about "good" and "bad" design, implying that in particular contexts certain arrangements may let you reap benefits while others tend to result in drawbacks.
That stronger flavor of "design" is also found in many other disciplines such as law, manufacturing of tools and appliances, usability engineering, game design, and marketing. Here the emphasis is put on intentionally influencing the behavior of users or participants in some favorable way. (The expected favorable effects may occur either for themselves or for someone else, e.g. the party who hired the designer; if a zero-sum game detrimental to the subjects of design is involved, one should more honestly speak of "manipulation" instead). One may also define "design" in a negative way and point out that it comprises all efforts to prevent, well in advance, undesired behaviors or events from occurring during operation of some system. Either way, the first step of design would be to explicitly identify the actors, the utility function that we want to optimize, and the purported causal relationships that connect designed elements to the actors' behavior and their behavior to the optimized function. These causal claims better be supported by empirical data! Thus, design involves meticulous planning and hypothesizing based on experience and facts. It also involves testing to verify the hypotheses. In short, it benefits from a scientific approach.
However, note that there's also a peculiar understanding of "design" proliferated by practitioners of "visual arts" - as found in the phrase "graphics design" and also worryingly often in "web design". This kind of design is indeed closer to "art" and "aesthetics" and satisfying creative whims rather than purposeful control toward achieving well-defined goals. Many a "web designer" is someone interested in (and hopefully proficient in) creating visually pleasing layouts of graphics and type. I do not wish to criticize the merits of such work in general. Printing and typography are both well-established and non-trivial crafts. I want to contrast them with the action-oriented forms of design mentioned earlier. There is not so much action involved in looking at a finely printed book page.
The foremost goal of an artist is not to optimize the performance of a particular task based on hard empirical data or to ensure that someone's sales targets are met. Rather, it is to evoke certain feelings, thoughts and emotions, to impress the viewer in a particular way, to visually communicate their own mood or state of mind, while perhaps following some specific self-consistent style. Even though emotions doubtlessly drive human behavior (possibly much more so than reason, on average), and even though you don't want your audience to experience negative feelings or be annoyed by botched aesthetics of your product, the causal connection of art-induced moods to identifiable sequences of actions and quantitatively measurable goals is notoriously hard to establish. Usually, it is not the "overall impressions", but rather specific actions induced in specific context that matter, the overall impression and "success" emerging as a sum of hundreds of subtle details done right. Not so for many artists who "succeed" in their own eyes, but still fail miserably on any other objective account, including on account of "design" in the above elucidated stricter senses of the word. If artists called themselves doctors, most of us would prefer to call them quacks.
In conclusion, when you decide to obtain advice from, or services of, a "designer", do pay attention to what they perceive as their job definition, especially to the extent in which they recognize the mundane, utilitarian aspects. Failing that, you might find yourself in place of an art patron rather than recipient of effective business services. Your return on investment may then amount to subjective satisfaction predicated on your own suspension of disbelief and submission to the artist's superior sense of authority. Don't let them fool you.