Difference between confirmation time and block generation time

I am currently trying to calculate the average transaction time over bitcoins history and have a problem with the definitions of "confirmation time" and "block generation time".

How I see it the block generation time is usually around 10 minutes and gets recalculated every 2016 blocks in order to be able to generate blocks at a steady speed. However this does not mean that your transaction is in one of said blocks.

The confirmation time however seems to be the time it takes for the network to take my transaction, put it in a block and then build at least one block on top of that block. So it is actually including the time my transaction spent in the mempool waiting to be picked up + around 10 minutes for the generation of the block with my transaction in it.

So if I make a transaction and I see 25 minutes as a confirmation time it should be 15 minutes spent in mempool, 10 minutes to generate a valid block and if I want 6 confirmations then I should add around 5 additional confirmations * 10 minutes = 50 additional minutes.

Is that correct?