It originally consisted of two branches, the domestic branch/Argent and the international branch the Suicide Squad. Those groups eventuality dissolved until Amanda Waller put together her own version of this team (legends mini series) utterly ruthless, totally expendable. And what you got was the kick ass regiment of killers from Ostranders celebrated run. Later Project Cadmus and Checkmate were added to TaskforceX. Cadmus as a high tech genetic and weapons research division
And Checkmate the worldwide charterd metahuman monitoring force whos operatives are modelled after pieces of a chessboard. One King one Queen and several Bishops. The Bishops oversaw the Rooks behind the scenes while the Rooks planned missions and supervised the field agents the Knights and Knights support paws. Now a new system is in place, the rule of two. Each superpowered or enhanced member in the Royal Family must have an unpowered counterpart in the same position of power.
The name TaskforceX has become synonymous with the Suicide Squad. But TaskforceX is actually a trinity of one. The operatives that work on behest of the government are called TFX. And those operatives that are deployed by Amanda Waller are called the Suicide Squad. The third group that operates as the Suicide Squad are employed or loyal only to Waller which is the true TaskforceX.