Are pictures saved using a digital camera stored as jpeg files?

Yes.

The most popular format for storing photos is the jpeg format which means the name of the file generated by the camera is most commonly something ending with the three letter jpg or JPG extension.

This is not true for all pictures on all cameras, just most cameras. The basic hand held "point and shoot" camera that can be purchased currently will store photos in jpeg format. Older cameras and more expensive cameras are more likely to have a different format. It is also true that the camera may be capable of storing the image in (or converting it to) several different formats based on the settings selected by the user.

The jpeg format saves space but it also removes details from the photo the camera has actually taken. Normally a typical camera employs one or three CCDs (charge coupled devices) to detect the light and record the image. That information acquired by the CCDs is a much larger, and requires typically more than ten times the storage than the jpeg version of the image. The reduction is size occures when the camera converts from the original raw image data to the jpeg format and when the encoding in jpeg takes place, information in the original image is lost.

The highest quality cameras, that a professional photographer might use, do not convert to jpeg but use other formats which retain more or all of the original information collected by the light detectors (CCDs). There are many other formats for digital images with advantages and disadvantages when considering the image quality versus image size issues and also the issue of image manipulation. One can literally write a book on the technicalities and uses of these many other formats, so that aspect of the answer is best done by a separate investigation by those interested.

Wikipedia has an extensive description of the jpeg format at the link below.