How many transition elements are there?
Shakespeare apparently said "What’s in a name? That which we call a rose, by any other word would smell as sweet." Rule no. 1, don't trust the internet until and unless you have some idea about the credentials of the website (and this comes with experience).

The usage of the term transition metal is nothing but historical. You can stick to IUPACs definition (https://goldbook.iupac.org/terms/view/T06456)


  An element whose atom has an incomplete d sub-shell, or which can give rise to cations with an incomplete d sub-shell.


By that zinc should not be a transition element. The definition has nothing to do with paired electrons as you wrote in the comments.

Look at the history of word, this is from 18th century from the unabridged OED.


  transition element  n. Chemistry  [after Russian perexodnyj èlement (see transitional element n. at transitional adj. and n. Compounds)] (originally, now historical) any of the nine metallic elements forming group VIII of Mendeleev's periodic table; (now) any of a large class of metallic elements occupying the central block of the periodic table (groups IV b–VIII, I b, and II b, or 4–12, the d-block), which are characterized by partly filled d orbitals, commonly show variable valency and an ability to form coordination compounds, and form many coloured compounds; often extended to include also those elements having partly filled f orbitals (the lanthanides and actinides).