As you say, the two plays were written at two very different historical moments. The Birthday Party was written in the late 1950s when the Cold War between the Western Bloc and the Soviet Bloc was reaching its peak. The threat of a nuclear war was a concrete danger at the time and Britain also had to cope with the fact that it no longer was the leading international power that it had been before the Second World War. The play reproduces this sense of constant menace as Stanley is persecuted throughout. The Birthday Party also mirrors the feeling of alienation and absurdity that the loss of a central position as world leader entails. The characters that populate the play are isolated from society and their communication is completely uneffective. The audience never has a clear idea about who the characters really are. These were the features that initially made the play a commercial and critical failures but that, with the passing of time, became the marks of Pinter's celebrated style.
First produced in 2000, Celebration was written in a significantly different historical context one that saw the end of the Cold War and the apparent triumph of the Western model of Capitalism. Yet, the play still emanates a sense of menace and the characters in the elegant West End feel just as threatened by their past and by the intrusion of a waiter who could unsettle their celebration. The characters are not the drop-outs of Pinter's first plays but members of the moneyed elite, unscrupulous behind their respectable facades.