The main difference is not what can be modified by the trigger, that depends on the DBMS. A trigger (row or statement level) may modify one or many rows*, of the same or other tables as well and may have cascading effects (trigger other actions/triggers) but all these depend on the DBMS of course.
The main difference is how many times the trigger is activated. Imagine you have a 1M rows table and you run:
UPDATE t SET columnX = columnX + 1
A statement-level trigger will be activated once (and even if no rows are updated). A row-level trigger will be activated a million times, once for every updated row.
Another difference is the order or activation. For example in Oracle the 4 different types of triggers will be activated in the following order:
Before the triggering statement executes Before each row that the triggering statement affects After each row that the triggering statement affects After the triggering statement executes
In the previous example, we'd have something like:
Before statement-level trigger executes Before row-level trigger executes One row is updated After row-level trigger executes Before row-level trigger executes Second row is updated After row-level trigger executes ... Before row-level trigger executes Millionth row is updated After row-level trigger executes After statement-level trigger executes
* Regarding what rows can be modified by a trigger: Different DBMS have different limitations on this, depending on the specific implementation or triggers in the DBMS. For example, Oracle may show a "mutating table" errors for some cases, e.g. when a row-level trigger selects from the whole table (
SELECT MAX(col) FROM tablename) or if it modifies other rows or the whole table and not only the row that is related to / triggered from.
It is perfectly valid of course for a row-level trigger (in Oracle or other) to modify the row that its change has triggered it and that is a very common use. Example in dbfiddle.uk.
Other DBMS may have different limitations on what any type of trigger can do and even what type of triggers are offered (some do not have
BEFORE triggers for example, some do not have statement level triggers at all, etc).