Learn English – Lift is for car so what is for bike

Yes, an automobile is only a "car", the kind of road automotive vehicle for passengers that was first built in Germany in 1889. Also the noun with this meaning was well established before the advent of aeroplanes and airships.

One early name for the new contraption was automobile carriage (German: Automobilwagen) perhaps not so not surprising since these vehicles looked very much like the carriages of the day.

Scientific American reported in Vol 77 "In 1894 a great impetus was given to the automobile carriage by a competition organized in Paris by the Petit Journal."

Very early automobile was used as a noun, also in popular literature:

"The automobile ran down the verge of the plain. Here a secure spot for a camp was selected." The Bradys in Frisco; Or, A Three Thousand Mile Hunt ([1899])

I believe the word take in, "let's take the car" is implying that you bring the car with you where you go. Get doesn't seem to connote this and thus doesn't seem to fit.