I am using SQL server 2008R2, but I am not sure I am using geometry or binary ... would anyone tell how I can find that?
There are significant differences between Geography and Geometry spatial types in SQL, and I'd by no means accept the "default" without determining what storage format best fits your data needs. Without going down the rabbit hole of this is better than that, check out Spatial Data Types Overview for a detailed description of both. It boils down to your choice of coordinate system and desired precision of measurements. Personally, I'm a fan of geography....
You can also look at the table from Management Studio. If the database reports the geometry column as an integer, then it's using SDEBINARY geometry storage.
Otherwise the DataType for the column will be geometry or geography for SQL Server spatial types.
You can check this from the table designer
select DATA_TYPE from INFORMATION_SCHEMA.COLUMNS where COLUMN_name = 'shape' AND TABLE_NAME = 'YOUR_TABLE'
I started looking into this question when reading the documentation for editing a versioned view with SQL:
The versioned feature classes you want to edit use a binary geometry storage type (when editing a named version)
If editing feature classes, the feature classes use SQL spatial types, not binary geometry storage (when editing the Default version)