A 'harrow' is a broad term, a 'disc' is a specific term.. thus a 'disc harrow is a type of harrow using disc's.
There are chain or 'drag' harrows which are flat mats made of link or chainwork.. usually have a n agressive and non agressive side, used mostly for covering seed, slight leveling or covering grad/box marks in prep for sod, or for busting dirt or maneuer clods.
There are also other harrow types.. like rotary units that have down pointing tines on a horizontal deck that rotates as the tractor moves .. horse areenas and 'rodeo' areenas ' usually employ this type.
Still there are others with tines, spring teeth or spikes.. etc... etc.
Some Harrows are very similar to cultivators and have some overlap in capabilities / duties.
Generally if someone said they 'disc'd' a pasture.. they used a disc harrow on it.
( to really mess you up.. there is a 'disc' plow as well as the conventional moldboard blow.. as well as middle busters, potato plows and sub soiler tye rippers.. etc.. )
Here's a like to a wiki reference to an agricultural harrow: not the best site.. but they get it right sometimes..
Harrow (tool) - Wikipedia, the free encyclopedia
Soundguy