La palabra "amuje" tiene dos acepciones.

La primera de ellas es como sinónimo de "esguín" y "murgón".

La segunda (la que nos interesa) es el equivalente de "smolt".

Véase la entrada "smolt" en:

http://www.termcat.cat/ca/Cercaterm

I am sorry, but I don't think "amuje" is the answer to this conundrum. Alistair's source, TERMCAT, gives it as a synonym of ES esguín and murgón, and equivalent to EN parr and smolt. But this lumps together different stages of development of the Salmon: parr and smolt are definitely not the same thing; parr is much younger. And it is given as equivalent to "salmó aleví" in Catalan.

I have found no evidence that "amuje" corresponds to a later stage of development than "esguín". Indeed, it is regularly defined as "alevín del salmón". What distinguishes "amuje" is that it is a local term, from Salamanca, for a young salmon ("cría del salmón").
http://www.google.es/search?q="amuje" "salmón"&hl=es&prmd=im...
Indeed José de Lamano y Beneite defines it in his Dialecto vulgar salmantino (1915) as "Especie de salmón que se cría en el Duero".
http://www.scribd.com/tourismaldeadavila/d/64967768-Dialecto...
So it's a river fish, anyway, which means it's not a smolt, which is a young salmon adapting to salt water.

A smolt is a salmon that has passed the river stage (2 years normally) and is getting ready to move into the sea:

"The next stage in a salmon's life is the smolt stage. In this stage the salmon's body is making the adjustment from fresh water to salt water as the fish is getting ready to enter into an estuary (where the ocean meets the river) and then into the ocean"
http://www.angelfire.com/ego2/salmonguy26/#Smolt

You are quite right that "esguín" and "murgón" are widely treated as synonyms. "Gorgón" is another term usually treated as having the same meaning. But there is a good deal of imprecision in general sources and dictionaries; they tend to treat a young salmon as a young salmon and leave it at that.

However, I have found an apparently reliable scientific source that distinguishes "esguín" from "murgón", and makes it clear that the latter is more advanced. It comes from the World Organization for Animal Health / Organización Mundial de Sanidad Animal (OIE), and is a chapter from its "Manual de pruebas de diagnóstico para los animales acuáticos" (2006) on the salmon disease Girodactilosis, caused by the parasite Gyrodactylus salaris. Here we read the following:

"Normalmente, la girodactilosis se produce cuando G. salaris está presente en el salmón del Atlántico susceptible, cultivado o silvestre, en la fase esguín de desarrollo o en la fase “murgón” juvenil en que inicia su adaptación fisiológica al medio marino."
http://web.oie.int/esp/normes/fmanual/pdf_es/2.1.14_Girodact...

Other parts of the essay make it clear that the "fase esguín" is the freshwater development phase before the salmon takes to the sea. "Murgón", however, is the (subsequent) phase of adaptation to salt water, exactly the definition of smolt.

I therefore recommend that "esguín" should be used for "fingerling" and "murgón" for "smolt".

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Note added at 4 hrs (2012-01-12 18:14:43 GMT)
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"Los salmones recién nacidos emergen del fondo de arroyos y de las playas, y pasan tres años en el lago antes de transformarse en murgones que migran hacia el mar"
http://books.google.es/books?id=HZaC45m9lMMC&pg=PA529&lpg=PA...

This is from a Mexican document:
"La exposición al herbicida FAENA® en agua dulce en concentraciones de 0, 10, 103 y 990 μg por 10 días no ocasionó ningún daño a los murgones de salmón para su adaptación al agua de mar."
http://sinat.semarnat.gob.mx/dgiraDocs/legamb/FAENA.pdf

"Se prepararán asimismo evaluaciones de impacto ambiental para el desarrollo de los tres nuevos estanques para murgones (smolts, según la palabra inglesa usada por la Compañía) conforme lo exige la legislación chilena."
http://spanish.iic.int/projects/view.asp?id=63&printview=1

"Necrosis pancreática infecciosa
Pero es una enfermedad que también provoca pérdidas considerables en los murgones de salmón atlántico al pasarlos de las aguas dulces a las saladas (Smail et al , 1989)"
http://www.oie.int/fileadmin/Home/esp/Internationa_Standard_...

Note that in all these cases, "murgones" are salmon that are ready to enter the sea, like smolts.

Concepción Ronda Laín, in her Glosario de términos en acuicultura (CSIC) distinguishes "esguín" from "murgón":

"salmón de un año; parr; esguín" (p. 66; parr = fingerling)
salmón joven; smolt; murgón" (p. 66)
http://books.google.es/books?id=K83oZtiheZcC&pg=PA66&lpg=PA6...