Technically no. Diameter is a specific type of width—the width of a circle measured through its center. Width is the general term for how fat something is from left to right. Think of it like this: all diameters are widths, but not all widths are diameters. It’s like saying all thumbs are fingers, but not all fingers are thumbs. Convince your thumb otherwise; I dare you.
Next time you’re measuring a round coffee table, or deciding if a lamp shade will fit, remember: you can call it whatever you want as long as the measurement works. The universe doesn’t care if you say “diameter” while holding a tape measure wrong. The universe just cares that your lamp shade doesn’t crash to the floor.
And if a math teacher ever corners you, just smile, nod, and say, “Of course, it passes through the center.” Then walk away, sip your coffee, and thank your lucky stars you never have to measure a pancake with a protractor again. Life’s too short for that kind of precision.