Basic Tornado Definition
To set the record straight, a tornado is defined as a violently rotating column of air, extending from the cloud base to the ground. A tornado will result in ground-based damage if vegetation and/or structures are present along the path of the tornado. However, there may or may not be a visible condensation funnel within the tornado, nor does the condensation funnel have to "touch the ground" in order to have a tornado.
In the absence of a condensation funnel, your only clue that you have a tornado is the observance of a ground-based, dirt/debris spray/swirl with cloud-base rotation above. In these cases the tornado may appear to be nearly invisible.
Most of the general public use 'tornado' and 'funnel cloud' interchangeably. This is understandable since, in general, public and private schools do not teach basic meteorology. However, equating 'tornado' and funnel cloud' is incorrect! These are two different animals within the severe weather world! Don't interchange these terms! You can't use both terms to describe the same event, it's one or the other!
Pictures of two different tornadoes are shown below: the first one has a classic "stovepipe-funnel" shape, but the second one is nearly invisible, save for the rotating dirt/debris spray-swirl at ground level and cloud base rotation (rotation not discernable in this static image.).
The picture below is labeled with the names of different features typically associated with super-cell thunderstorms. Super-cell thunderstorms produce most of the tornadoes in the U.S, and always contain a rotating updraft. This is a picture of a still potentially tornadic storm when it was over southwestern Green Lake County. A few minutes prior to the time this picture was taken a tornado moved through southeastern Marquette County into southwest Green Lake County on July 27, 2009.
Again, there is no visible tornado in this picture. Usually, but not always, a tornado will develop underneath or very close to a rotating wall cloud. To the left of the rotating wall cloud is a shelf cloud associated with the Rear Flank Downdraft (RFD) that is coming around the rotating wall cloud. Remember, some cloud fragments associated with shelf clouds may briefly resemble tornadoes or funnel clouds. However, they are not true tornadoes or funnel clouds since they don't possess persistent rotation and there is no damage.
In the picture below - the very low, horizontal, inflow cloud band to the right of the rotating wall cloud indicates strong in-flow into the base of the storm from the right. In-flow cloud bands can be very close to the ground and also look scary.