The term "Starday" has been universally accepted to mean birthday, since it's mentioning in the similarly named TV episode. However, there was a refrence to birthdays much earlier in the franchise.
In LBT5, when the gang was walking to the Mysterious Island over the land bridge, Cera griped, "Its like waiting for your hatch day, it never seems to get any closer!"
To be honest, the first time I heard this line, I thought she meant the actual day that one hatches out of their egg, (for example, mine would be December 8 1988, as opposed to just December 8). For the next few minutes untill the giant wave blasted it's way on screen and drove all else from my mind, I was sitting thinking about the implications of this statement (does that mean unborn dinosaurs are in their egg, already awake and thinking before they hatch? What would it be like to be trapped in an egg like that for so long? Would they really think of their hatch day in relation to 'closer,' not knowing what hatching is yet?) Soon after, some slightly more logical part of my brain took over, and I realized she might have just meant every generic birthday, and immediately dropped all the intriguing thoughts about being trapped in an egg, waiting for days on end for the Hatch Day to arrive.
However, then the TV Series came along, and this new episode established very clearly and indisputably that a birthday is known as a Starday, not a Hatch Day.
Does this mean that a Hatch Day could really refer to just the day of hatching, and only the day of hatching? Would that mean Cera's statement shows that, in the LBT universe, unborn dinosaurs are still awake and aware of their surroundings while still in their egg? I know the producers probably were not meaning to imply this, but it's a really interesting idea all the same.