It depends.
If the card is like B.E.S. Crystal Core or Ancient Gear Castle, the Counters referred to by those cards are just generic, no-named Counters.
If it's a card like Counter Cleaner, that will affect Counters of all types, named (Spell, A, Venom, etc.) and unnamed (like those mentioned above).
Otherwise Named Counters simply have that designation so that other card effects can work with them (Like Aliens and A Counters, Pitch Black Power Stone and Spell Counters, etc.)
