Without caustics, an object cannot transfer its colour to the light passing through it.

I can see something on the square in the Poser render - illumination from the light. Did you set Cast shadows on the square? Is the render Cast shadows option switched on? If you are using RT shadows, is RT switched on?

Carrara is showing illumination plus shadow from the transparency map, which is why it is inverted. With white light and white surface, this can only ever be grey.
 
I thought Carrara supports caustics.

"If I were a shadow, I know I wouldn't like to be half of what I should be."
Mr Otsuka, the old black tomcat in Kafka on the Shore (Haruki Murakami)