This is in line with the dictionary style. The entry would have been formatted like this if we were trying to indicate they were 2 
different species:
[1][n][uk]
  Japanese tit (Parus minor)
[1][n][uk]
 Oriental tit (Xxx xxx)

Rather looks like it is referring to two different species, covered by the same word, rather than it being an alternative name.

GG5 (obviously a bit dated): 【鳥】 a (Japanese) great tit; Parus major; 〔欧州産の〕 a great titmouse; 〔米国産の〕 a chickadee.

We usually put alternative names after the main one.

@@ -25 +25,2 @@
-<gloss>Japanese tit, also known as Oriental tit (Parus minor)</gloss>
+<gloss>Japanese tit (Parus minor)</gloss>
+<gloss>Oriental tit</gloss>

https://en.wikipedia.org/wiki/Japanese_tit
https://en.wikipedia.org/wiki/Great_tit
https://ja.wikipedia.org/wiki/シジュウカラ
https://www.researchgate.net/publication/229514602_The_great_tit_Parus_major_-_A_misclassified_ring_species
http://www.worldbirdnames.org/bow/waxwings/ (search for "parus major" or "parus minor". It is noted where they are, and Major isn't anywhere near Japan)
http://www.catalogueoflife.org/col/details/species/id/a0aec8cac12ff745bf4a69f56fdfa1cb

http://gogen-allguide.com/si/shijyuukara.html (to establish, if it was needed, that the name is quite old indeed. Also that it is ateji)

The Japanese/Oriental tit (the former seems like it may be more common, though the latter makes more sense. Also known as Eastern Great Tit, which also makes more sense, in at least one source …but as I said. Japanese tit seems to be the more common/established name) was long thought to be a sub-species of the Great tit. (Parus Major Minor)
Hence the definition here, as Great tit, is perfectly understandable.

This has, however, been shown to be wrong, for several years now. More up-to-date sources, correctly list it as a separate and distinct species, Parus Minor.
This old Japanese name, is clearly one that was used to refer to the native birds (i.e. Japanese tits), and not the foreign, if similar, Great tit.

(I've done a quick search, to find a common name for the Great tit, in Japanese, but couldn't find anything. I'll maybe try some more, but maybe it doesn't really have one, yet)

Also, the しじゅう comes from the sound of the birds song, and has nothing to do with 14 (四十), and hence ateji.

@@ -5,0 +6 @@
+<ke_inf>&ateji;</ke_inf>
@@ -24 +25 @@
-<gloss>great tit (Parus major)</gloss>
+<gloss>Japanese tit, also known as Oriental tit (Parus minor)</gloss>