All lightbulbs have different primary colors, depending upon the type of bulb they are. Our eyes can't always perceive the color differences (though sometimes they can), but they do make a world of difference to a camera. The "soft white" incandescent bulbs tend towards yellow, "daylight" indandescents towards blue, standard flourescents towards green, etc. Not only that, but the construction of your camera's body and lense can make a huge difference, too. I bought a point-and-shoot type of digital camera that is waterproof. I bought it when it first came out on the market, so there were no user reviews available. However, six months or so later, there were tons of reviews on it - all complaining about the needed light conditions to yield decent pictures. Apparently how this camera was constructed in order to be waterproof is impacting it's light intake.
You should also be aware that digital cameras can have a "white balance" issue - if you have manual override capability, you can play around with the white balance setting to get your whites truly white. Otherwise, your whites may end up very blue (or other colors, but blue is most common.) Most point-and-shoot digital cameras don't allow white balance adjustment, though some do.
So yes, the type of lighting you use as well as camera construction will impact your pictures. Often bringing in additional light with a different color tendency will help to offset the negative effects of your usual light. For example, I use a halogen desklamp or two when taking food pics for the cooking threads, and I've found that helps offset the combo of kitchen light and flash from the camera that frequently makes my pictures ridiculously dark. It's not 100% foolproof, but it does help.