Confusion over the term "family crest" probably arose from an understandable abbreviation of the terminology in heraldry for an important part of a coat of arms. One of the most respected sources for heraldry information is Fairbairn's Book of Crests of the Families of Great Britain and Ireland, first published in 1859 and revised over the years in various reprints. It is not difficult to see how the use of the term "crest" could have become synonymous in common use with the term "coat of arms," since one is a part of the other. Through time, "the crest" has been associated with family names, independent of the coat of arms, in such publications as Fairbairn's.
Gaelic tradition allows family members to use of the "crest" part of an entire coat of arms (that which appears above the shield) in a badge setting (a circular belt), thus all members of a given clan are entitled to use the clan badge.
Coats of Arms and Crests Belong to Individuals, Not Surnames
Coats of arms are not awarded to a family or a name, but to an individual. There is often more than one coat of arms associated with a given surname. In England, direct descent is required for any heir to have the legal right to bear his ancestor's coat of arms. You can try to narrow the search by geographic region of origin, but there may also be more than one coat of arms awarded to several people in ancient Germany. Further complicating the issue is that the authoritative source information for most coats of arms only lists a city and/or county or origin, and sometimes only a country. That is why, unless you can trace your family history to one individual, and unless the sources list that individual, then the best that you can hope for is to find a coat of arms that is the oldest for a given name from a given region or the one most frequently used. Coats of arms usually started out fairly simple in design, subsequent generations added onto or made slight variations to the design to make it their own. Marriages often resulted in a combination of two different family lines' coats of arms.
The bearing of coats of arms is not regulated in most countries, including the United States, thus there has been a proliferation of "family name" companies offering histories and coats of arms for a given surname. While there is no reason we cannot enjoy the decoration of a coat of arms associated with someone centuries ago who shared our surname, we should be aware that this is all that it is -- a decoration.
There is also no reason we cannot create a coat of arms and crest for ourselves, whether based on the coat of arms of an ancestor who shared our name (and may or may not be related to us), or designed from scratch to mean something special to our own lives and family.