An audio cassette is a cassette containing audio data.

1963 Philips introduced the compact audio cassette medium for audio storage in Europe in 1963, and in the United States in 1964, under the trademark name Compact Cassette. Although there were other magnetic tape cartridge systems, the Compact Cassette became dominant as a result of Philips's decision in the face of pressure from Sony to license the format free. It went on to become a popular (and re-recordable) alternative to the 12 inch vinyl LP during the late 1970s. source: wikipedia article for Compact Cassette.

Similar only in the fact that both can be used to record audio. However, their underlying technology is totally different. A cassette records audio in an analog format while a CD records audio in a digital format.

Compact Cassette was created in 1963.

Digital Compact Cassette was created in 1992.