distinguish will always link to the provided page names:
{{distinguish|PAGE
}} gives distinguish|PAGE|PAGE1
}} gives
{{distinguish|PAGE|PAGE1|PAGE2
}} gives
{{distinguish|PAGE|PAGE1|PAGE2|PAGE3|PAGE4}}
gives
distinguish2 only accepts one parameter and does not create a link by default. To do so add the link yourself. It may contain an anchor and pipe.
{{distinguish2|PAGE
}} gives {{distinguish2|[[PAGE]]}}
gives:
{{distinguish2|[[PAGE|other page]]}}
gives:
Each parameter must be a valid pagename and must not contain links or wiki markup.