At one level, a person could look up fascinating and interesting in, say, Merriam-Webster's Eleventh Collegiate Dictionary (2003) and find these entries:
fascinating adj (1638) : extremely interesting or charming : CAPTIVATING
interesting adj (1768) : holding the attention : arousing interest
Those definitions are, as Mr. Spock might say, interesting but not fascinating. They indicate that people may use fascinating to convey the idea that something is at the high end of interesting or, on the other hand, that it may involve some level of involuntary appeal. But the two definitions in this general reference offer only a very brief description of how the words differ in practical meaning, and provide virtually no discussion of any underlying difference in tenor or implied direction that they may possess.
To get a sense of those differences, a person might consult Merriam-Webster's Dictionary of Synonyms (1984), which goes beyond the general-reference dictionary to identify a group of words that a particular word falls into. As it turns out, MWDS puts fascinating and interesting in different groups of synonyms.
Fascinating appears in a group with charming, bewitching, enchanting, captivating, alluring, and attractive, with a link to the following discussion of the verb form fascinate in an entry under attract:
Attract, allure, charm, fascinate, bewitch, enchant, captivate mean to draw another by exerting an irresistible or compelling influence over him. The same distinctions in implications and connotations are observable in the adjectival forms of these words, attractive, alluring, charming, fascinating, bewitching, enchanting, captivating. ... Fascinate, like charm, implies the casting of a spell, but it usually suggests the ineffectiveness of resistance or helplessness to escape from from the one that fascinates [examples omitted]
Interesting, meanwhile, appears in a group with engrossing, absorbing, and intriguing, with this comment about what the words have in common:
interesting, engrossing, absorbing, intriguing mean having a quality or qualities that secure attention and hold it for a length of time. Interesting implies a power in a person or thing to awaken such a mental or emotional reaction involving attention as curiosity, sympathy, a desire to know or understand, or enthusiasm, but unless the adjective is qualified or there is a fuller explanation in the context, the degree or the cause of interest is not clear [examples omitted] As applied to a book, a play, or a narrative the word usually means entertaining, diverting (compare verbs at AMUSE) exciting, stimulating, or provocative (compare verbs at PROVOKE), but if the context provides no real clue as to the precise implication, the word may fail to hit the mark.
So the essential difference in the orientation of the two words, according to MWDS is that fascinating at its core involves attraction whereas interesting at its core involves attention.
S.I. Hayakawa, Modern Guide to Synonyms and Related Words (1968) provides a somewhat dated but still useful treatment of the adjective fascinating (which Hayakawa bundles with charming, bewitching, captivating, enchanting, entrancing, and winning) and the verb interest (which he bundles with entertain, amuse, and divert):
charming [etc.] All of these words are superlatives used mainly to describe the pleasing manner of an attractive person, usually a woman. ... Fascinating has perhaps suffered less from overuse as a superlative than these other words. Although more general in application, it still can suggest, like entrancing, a prospect that is almost hypnotic in its inviting quality. It applies to men as well as women, to any attractive scene or view, or to any idea or thing that is extremely interesting. In all cases it is like captivating and winning in suggesting the ability to overcome resistance, however strong: [example omitted].
entertain [etc.] These words have to do with activity that draws the attention and makes time pass agreeably. ... Interest is the most general of these words. To interest someone is to excite or hold his curiosity or attention, for whatever reason. [Examples omitted.] But the specific sense in which interest compares with the other words in this set involves an awakening of attention by some entertaining expedient: [example omitted].
Once again, as with *MWDS'*s treatment of the two words, the essential difference seems to relate to the notion that fascinating is based on attraction and interesting is based on attention.
Ultimately, all questions about the differences in meaning between two words are susceptible to the criticism that the question asker should simply have looked up the two words in a dictionary and see how the definitions given there differ. In my view, this argument gives short shrift to the complexity and subtlety of word meanings and word usage.
I think that consulting reference works that focus on distinguishing particular words from others with similar meanings is a far more fruitful way to reach an understanding of how two words differ in meaning than simply checking the entries for the two words in a general-reference dictionary of the sort that any visitor to English Language & Usage may be fairly presumed to possess. Indeed, the reason that the "differences" tag isn't banned at EL&U is that in many instances a general-reference dictionary is not especially helpful in clarifying such differences.
For these reasons I completely agree with Dawson Baker that it is a mistake to assume that a general-reference dictionary will satisfactorily answer a serious question about the differences in meaning between two words.