The common definition I use is:
A type coin is a representative coin from a given series. Type coins are collected based on the series they exemplify instead of its date and mintmark.
The trick here is the word "series". I've seen no official definition of a series so it is a perspective based definition. In that light, Prethen is is absolutely correct.
Now if we are talking about coin advertisers that sell "Type Coins" the general definition of a series is defined by a combination of coin design & denomination and it can be any coin representative of the series regardless of date or mint mark (sellers only sell common year/mint marks as types). For example:
A Barber Type Dime would be any example from 1892 to 1916 and may be any mint mark. The retailer would probably ship a 1913P or 1915P dime as these are pretty common (and there is zero chance that they will ship a coveted 1895-O key date dime so don't hold your breath).
If your goal is completing a type set then this is a fine approach as they do the hard work of finding the coin for you. If you were looking to complete a type set with some hopes of $$ value growth then it is the wrong approach as common coins do not appreciate as fast.