Nominal & Real GDP vs Laspeyres & Paasche

Is the GDP deflator the same as the Paasche index?

How are these four measures of economic value related?

GDP deflator is factor by which you bring the nominal GPD to the real GDP. It shows how much the base year’s GDP changed due to changes in price.

The Paasche Index is a way you can calculate inflation using a basket of goods. Normally, the most common method of doing this is keeping the content of the basket of goods constant and just measuring the overall price movement of that basket of goods (Laspeyres index). The Paasche index allows for greater flexibility and you use the current year’s basket of goods instead of that constant amount.

Hmm never thought about it but I believe the derivation is the same or very similar between the two:

Current Quantity (aka Consumption) x Current Price (aka Nominal Price) / Current Quantity (aka Consumption) x Base Price (aka Real Price)

Anyone else care to confirm?

This is why I ask. The only difference I can think of is the base year. Paasche index might go from year to year without skipping (ie. 2012 to 2013). GDP deflator might always use a base year of 1990.