What is the signal transduction pathway in which multiple signals lead to the same type of protein product?
A convergent signaling pathway.
A convergent signaling pathway is a pathway in which signals from different types of unrelated receptors all signal to a common target.
An example is the signaling to the protein BAD that promotes cell survival. The image below shows this pathway. Don't mind all the terms, just look at the big picture. Three different signaling pathways all converge to the BAD protein.
There are many more examples of convergence, though most often there is a very complex crosstalk between different signaling pathways, converging and diverging.