There are three types of Solar Eclipses. The most commonly seen is the Partial Solar Eclipse (PSE). During a PSE only a portion of the Sun’s surface will be covered. It will appear as if a large bite has been taken out of the Sun.
When the bright surface is completely covered a Total Solar Eclipse (TSE) is taking place. Surrounding the shadow of a TSE is a PSE. Thus one sees a partial eclipse up to the total eclipse and then a partial eclipse afterwards. Only during a TSE is it safe to look at the Sun. Then you can see the corona and prominences.
If the cone of the shadow from the Moon falls short of the surface of the Earth then an Annular Solar Eclipse (ASE) takes place. In an annular eclipse the surface of the sun is obscured across the mid section but there is still a ring of photosphere visible. It appears as a ring of file and causes very odd donut shaped pin hole projections. Like a TSE, there is a PSE surrounding the ASE location.
The technical definition of a total solar eclipse is one where the umbra shadow from the Moon extends past the central axis of the Earth. When the shadow does not touch the surface of the Earth the eclipse is considered annular. That means there is a grey area where an eclipse might start annular, then be total, then annular again as seen from different points of the Earth. Those eclipses are considered Annular/Total Solar Eclipses (ATSE) or Hybrid Solar Eclipses (HSE).