GetScalar is the generalized form, and GetDBCount is the special case.
In fact the following:
var cusomers = new EntityCollection<CustomerEntity>();
var count = adapter.GetDbCount(cusomers, null);
Produces a Select Count(*) as seen below.
Query: SELECT COUNT(*) AS NumberOfRows FROM (SELECT [Northwind].[dbo].[Customers].[Address], [Northwind].[dbo].[Customers].[City], [Northwind].[dbo].[Customers].[CompanyName], [Northwind].[dbo].[Customers].[ContactName], [Northwind].[dbo].[Customers].[ContactTitle], [Northwind].[dbo].[Customers].[Country], [Northwind].[dbo].[Customers].[CustomerID] AS [CustomerId], [Northwind].[dbo].[Customers].[Fax], [Northwind].[dbo].[Customers].[Phone], [Northwind].[dbo].[Customers].[PostalCode], [Northwind].[dbo].[Customers].[Region] FROM [Northwind].[dbo].[Customers] ) TmpResult