Non-smart bulbs generally have a fixed color temperature, as you must know. Most smart bulbs that allow you to do color also allow you to do "shades of white," i.e., go into the non-color mode (CT mode) I mentioned above. There are some exceptions, like the first-generation Hue Lightstrip that don't have a good mix of LEDs to let you do much with white light; those are color only. Most can handle both. Some can only handle color temperature (e.g., Hue White Ambiance, Sengled Tuneable White, etc.), and others can't do either and are fixed like a "dumb" bulb (Hue White, Sengled Soft White, Sengled Daylight, etc.).
What a bulb allows you to do depends largely on what LEDs the manufacturer used and how well they can represent shades of white or color, but again most color bulbs allows you to set things in either "mode" (only one of which the bulb will consider active at a time). Ultimately it also depends on what Zigbee clusters the firmware implements. There are odd exceptions, like the Ikea Trådfri color bulbs that only allow color and don't implement the Zigbee color temperature clusters despite being able to do them quite well (in fact, their colors are a bit lacking and whites are pretty good--which you can emulate with great difficulty by finding hue and saturation values that approximate what you might get from certain color temperatures; the Ikea Smart Home app even lets you set them to white, presumably doing its own RGB thing behind the scenes).
