I don't think there's any fixed relationship between the number and distribution of tests and scenario tests.
I think the most common code-representation of a scenario is a specific set of business data required to support a specific story (scenario). This is often provided in the form of database data, fake stub data or a combination of both.
The idea is that this dataset has known and well-defined characteristics that will provide well defined results all across a given business process.
For a web application I could have a single web-test (or several for variations) that click through the full scenario. In other cases the scenario is used at a lower level, possibly testing a part of the scenario in a functional test or a unit test. In this case I normally never group the tests by scenario, but choose the functional grouping of tests I normally use for unit/functional tests. Quite often there's a method within "Subsystem1Test" that is called "testScenario1" or maybe "testScenarioInsufficientCredit". I prefer to give my scenarios names.