Both woodcut and linocut are graphic techniques, printing techniques.
Woodcut printing / woodblock printing is a very old graphic technique. A pattern is cut or curved out of wooden board or block. All the surfaces that are not curved or cut, are to be covered with ink / paint in order to make a print.
A sheet of paper, rice paper, silk (see Japanese prints) needs to be put on wooden board and pressed hard manually or in a special press. The print is a mirror image of the cut pattern. Linocuts appeared much later, after linoleum was discovered. The technique is very close to woodcut. Instead of wooden board artists started to use linoleum which is much softer, so it is easier to be cut. Woodcut and linocut prints look very similar, sometimes it is very difficult to see a difference.
Woodcut prints are known all around the world, we could see beautiful examples of art made with this technique in both Europe and Asia. I would recommend to see works by German artist, Albrecht Durer (1471-1528) to get known European woodcuts. And afterwards, do not hesitate to see old Japanese masters such as Hokusai (?1760-1849), Hiroshige (1797-1858).
In the 20th century for instance artists Oskar Kokoschka (1886-1980), George Grosz (1893-1959), created many woodcuts and linocuts.