Ok, that title sounds silly, but it’s actually a real point. The first parameterized refers to using parameters within dynamic SQL, while the second refers to how the optimizer treats parameters differently from variables. When you use parameterized dynamic SQL with sp_executesql SQL server treats the parameters as actual parameters not variables. As with all things, an example would probably help here.

-- Setup
SELECT * INTO myColumns FROM sys.all_columns
ALTER TABLE myColumns ADD CONSTRAINT pk_myColumns 
PRIMARY KEY (object_id, column_id)
CREATE INDEX ix_myColumns ON myColumns (name)
I’m using a very simple table, taking the data from sys.all_columns, with a pretty basic clustered primary key and index.
-- Code
DECLARE @name varchar(50) = 'name'
SELECT *
FROM myColumns
WHERE name = @name
DECLARE @sql nvarchar(1000) =
'SELECT *
FROM myColumns
WHERE name = @name'
EXEC sp_executesql @sql, N'@name varchar(50)', @name
The query plan for the first query
The query plan for the second query
What’s the difference?! Well, when you use a variable the optimizer uses an average value for the estimated number of rows (this is my best understanding and I could be miss-representing what’s actually happening but I don’t think so). When you use a parameter the optimizer can actually check the histogram and give an estimate based on the contents of the parameter. Here are the estimated and actual number of rows for each. 
Variable version:
Parameter version:
You’ll notice that the parameter version has a much closer (exact even) estimate of the number of rows.  
Also if you look at the query plans you’ll see that the variable version shows as a smaller part of the plan (7%/93%), and yet, when I timed them they were pretty close on time (590ms/731ms). I mention this not because the variable version is normally faster, but because I want to point out that these are estimates, and not necessarily all that accurate.