Yes, I seem to recall those phrases describing something different.
Generation X, the kids who reached their teens in the early to mid seventies through to mid eighties when the economy started to turn and unemployment started to rise, especially for those just coming onto the labour market who found themselves increasingly out of work, as in the punk generation. Those born around 1955 to 1975.
Generation Y, also known as the slacker/stoner generation. Around 1980 to 1995. Those who missed the downturns of the 70s and 80s and came into work when the labour market was better and youth unemployment was much lower than for generation X. Generation Y were also said to be the new, more materialistic generation. Which is certainly true. However, in that generation were a group being over educated for the jobs they found themselves in and finding themselves as (stereotypically) media study graduates doing 'McJobs' and flitting between low paid jobs while possibly getting stoned quite often.