This is certainly confusing, mainly because "fondo" can mean so many different things. Obviously background, in some cases. Also "base": in catalogue descriptions of ceramic items, for example, you find "fragmento de fondo" and "fondo completo", as well as "fragmento de borde", for example.

And then "fondo" in museum contexts can mean a collection, and as you say, that makes no sense here.

"Fondo completo" occurs very frequently in entries in the standard museum cataloguing system used in Spain, known as CERES (Colecciones en Red):
http://ceres.mcu.es/pages/SimpleSearch?index=true

And since this cataloguing system has been adopted by museums across the country, their own catalogue entries for particular items use this expression too. But they don't explain what it means.

However, I think it can be deduced from certain examples. This one is a drawing by Sorolla mounted on card (3rd item on page, click on "Ficha completa" to see full record):

"Materia/Soporte Papel Bristol [Pegado sobre cartón. El papel es de menor tamaño que el cartón. Las medidas son del fondo completo, es decir, del cartón.]
[...]
Dimensiones Altura = 61,30 cm; Anchura = 41,20 cm"
http://ceres.mcu.es/pages/ResultSearch?Museo=MSM&txtSimpleSe...

And this one is a photographic "performance", consisting of a series of photographs:

"Dimensiones Altura = 137 cm; Anchura = 1483 cm
Fragmento: Altura = 32 cm; Anchura = 26 cm
[...]
Clasificación Razonada La esfinge es una performance que genera un documento fotográfico, que a su vez puede presentarse como una colección de fotografías. El número de piezas va aumentando conforme se vuelve a realizar la performance.
Las medidas del fondo completo coresponden [sic] a la instalación de la obra completa con una separación media entre los elementos de 15.5 y 16 cm."
http://ceres.mcu.es/pages/Main?idt=123863&inventary=CE0260&t...

The "fondo completo" dimensions are those of the complete work as presented, as opposed to the dimensions of each "fragmento".

One more example, using the same terminology, but not from CERES. This is a work consisting of a pair of photographs:

"Dimensiones:
[Fondo Completo] - Altura: 70 cm
[Fondo Completo] - Anchura: 219 cm
Pieza izquierda - Altura: 70 cm
Pieza izquierda - Anchura: 145,8 cm
Pieza izquierda - Grosor: 3 cm
Pieza derecha - Altura: 68 cm
Pieza derecha - Anchura: 70 cm
Pieza derecha - Grosor: 3 cm"
http://fundacionhelgadealvear.es/wp-content/uploads/2011/01/... (p. 138)


So I think it's clear that "fondo completo" means a complete item in a museum collection, as opposed to a part or fragment of an item. And in the case of your coin it simply means that this coin is classified as a complete item and not as part of a larger item.

An example in English;

"Textile fragment with S-shapes and stylized leaves, possibly a trouser tie-belt
Unfortunately only the decorated part of the textile has been preserved so we cannot tell how long the complete item was originally. It is one of the many embroidered fragments in the collection from the ends of girdles."
http://jameelcentre.ashmolean.org/collection/7/1252/1253/all...