Collioure Lighthouse revisited - a mystery

Summer holidays spent in south west France, we revisited Collioure, which I had bagged as a lighthouse here.
As you can tell, the lighthouse in 2007 is not the lighthouse above. Basically, there is an inner harbour at the end of which there is a church with tower. If you go around the church there is an outer harbour, at the end of which is the structure above. The two 'lights' can both be seen better below.

Now the Lighthouse Directory lists the smaller light as the lighthouse, at the end of the outer harbour. Built in 1886, it is made of stone and cast iron.

So the peach-domed structure of my original post and in the picture above is not a lighthouse? Fair enough.

Except that everywhere it is referred to as Le phare (the lighthouse) Postcards all describe it as Le phare, Matisse has a famous painting (which I'm not very impressed by!) of Le phare a Collioure. Sometimes it is called a cloche / phare (bell tower / lighthouse)
The thick plottens.