A feed-through has the incoming power connected to the bus bars, and the conductors going to the downstream panel are also connected to the bus bars. In a sub-feed panel, one of its breakers will be used to provide the connections to the downstream panel. The use of that breaker is the difference in the two types. In both cases, the bus bars of the first panel carry all the current of the first panel, plus all the current of the downstream panel.
There is a third type, called a "double lug." The point at which the incoming conductors connect to the first panel has two sets of lugs. One to connect the incoming conductors, the other to connect a set of conductors going to the downstream panel. Here, the bus bars of the first panel do not see the current from the second panel.
Sub-feed and thru-feed do not have single universally accepted meanings. And the meanings can change slightly when discussing sub-feed lugs versus sub-feed breakers and main lug only panels versus main breaker panels.
For example, this is the explanation from the squared/com FAQ's:
"Sub feed lugs are for Main Lug Only panels and are located at the main end of the panel.
Thru Feed Lugs are typically for Main Breaker panels and are located at the end of the panel opposite the main breaker."