Identification: Kindly confirm or correct the ID of two mushrooms please

These two mushrooms grow side by side; seen on Mayne Island.
I labelled the skinny grey one as Coprinopsis lagopus,
and the large whitish one as Stropharia ambigua.
Kindly confirm or correct my ID please.

 

Hi David,

I agree likely Coprinopsis, but I am not certain of species.

The pale whitish yellowing one is not Stropharia ambigua: The habitat would make sense for Stropharia, but some other characters to note here that would exclude S. ambigua include spore colour (likely brown not black, check cap underneath another cap), overall size (S. ambigua is larger and stipe longer in comparison to cap width), cap texture (fibrils vs. smooth S. ambigua). While there are other Stropharia species, and given that I can't be certain of your spore colour, I am thinking that this looks more like an Inocybe.

 

Thank you Frog for the correction and clear explanation. Much appreciated.