Velatura and sfumato are two painting techniques first explored during the Renaissance; they are most often associated with oil painting. Both techniques are methods used to manipulate underlying layers of paint at any point in the painting process; they differ in the way they are applied and which artists explored them.
One of the four painting methods credited as originating during the Italian Renaissance, sfumato comes from the Italian word "fumo," which translates to "smoke." This technique is used primarily in oil painting to subtly blend colours, but it is not a glaze over the entire image. The use of sfumato led to works without hard lines or edges between objects, unlike the style of paintings prior to the Renaissance.
Like sfumato, velatura refers to a subtle method of adjusting colours. Velatura is unique however, in that it is an application of a glaze, specifically one that is applied with the artist's fingers. This technique is usually employed with translucent glazes over a layer of paint that is already dry. To properly create the velatura style, glazes must be diluted with a medium such as oil. Velatura was a technique used in previous artistic movements and is considered somewhat out-of-style.
Sfumato is perhaps best known as one of Leonardo da Vinci's favourite techniques. Two of his works -- The Virgin of the Rocks and the Mona Lisa -- employ sfumato extensively; the gentle shading in the Mona Lisa's face is an example of this. Other artists known for their mastery of the sfumato technique are Giorgione and Correggio, both active during the Renaissance.
The velatura technique was most famously used by both Titan and Velazquez. In the portrait of Innocent X by Velazquez, however, the glazes are notoriously difficult to photograph; thin paint in a velatura technique oftentimes appears to be thick in photographs, which makes observing this technique most effective in person.