Your Colonial-era 1-piece "flatbutton" is made of a metal called White-Tombac, not silver. White-Tombac is an alloy of approximately 90% copper, 8% zinc, and 2% arsenic. The presence of arsenic in the alloy made the alloy's color silver-ish. See the third button (and info) in the chart attached below.
And yes, your button's edge was broken off, not "made that way." White-Tombac is a more brittle metal than pure copper or brass... so we diggers sometimes find ones that are broken, like yours.