If I recall correctly, the first series of Airbuses were the A300/A310 series - waay back in the '70s/'80s. 

At that, the overall shape of the Airbus(es) follows the shapes of the Dassault Mercure (largely unssuccessful due to short range philosophy tankage).

You probably don't see many of them anymore because they're older planes, and heading to secondary lines/carriers.

The A310 was launched in 1982 as a direct derative to the longer A300 series.
One of the differences compared to the A300 is clean outer wing areas (without vortex generators) which results in a slightly higher lift coefficient.
The A310 was Airbus answer to the upcoming market of 200 seaters for the short haul/medium range market.

Yes the A310 is used to cross the atlantic, but that's the A310-300 which is the "long range" version with drag reducing wingtips (retrofitted on all 310's) and a tail plane trimtank to accomodate more fuel.

On the paper, the A310 was supposed to come in 3 different versions
-100 =short haul
-200= medium haul
-300= long range
Though the -100 series was dropped in favor of different weight versions for the A310-200.

It shares many traits with the A300, which means no FBW and conventional yoke and "strings" to rudder and other control surfaces 

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Quite similar to several undeveloped HS designs of the 1960s too. Have to say its had quite a good innings considering the later Airbus' and Boeing competition, and now enjoying a second life with several airforces as a tanker and transport aircraft