A Public Service

He pushed the button, which was red.

There was a button.
The button was red.
He pushed it.
Use a comma.

He pushed the button that was red.

There were buttons.
One of those buttons was red.
He pushed the red one.
No comma.

The comma separates the initial phrase from another extra bit of information about the thing. In the first case, “which” stands in for “the button”. It’s like saying, “He pushed the button. The button was red.”

In the second case, there is no comma, because “that” is used as a limiter, not a reference. It’s like saying, “He pushed the button. That button, the one that’s red.”

When you say “that one”, you point. You are limiting the referent.

To make things more confusing, “which” can actually be used as a limiter, and sometimes limiters can be used to add information. But when in doubt, follow these rules.