>>4
I have never played it, but what I've read on Wikipedia does not suggest too obvious similarities.

First and foremost, Elite is a single-player game played without an internet connection. All ships other than your own are computer-controlled. Eve Online is a massively-multiplayer online game, with all the social interaction, collaboration and competition between players this implies.

Eve Online star systems are connected by stargates, whereas Elite allows you to travel to any other system within a 7-light-year radius using your ship's internal hyperdrive (or travel to another galaxy using the galactic hyperdrive). I have not played enough Elite to find out whether it is possible there as well (although it should be), but in the remake Oolite ships travelling to another star system open a short-lived wormhole, which other ships can use to follow them without using any fuel, even if they are not themselves capable of independent hyperspace travel.
Eve Online has several playable races (I was unable to find out whether these affect gameplay or are merely cosmetic). Elite, while in theory having many different species, identify the player with the ship he currently owns (only one ship at a time; is this different to Eve?), and the only truly alien race are the always-hostile Thargoids. Also, Eve has a skill-point system whereas Elite relies wholly on the player's piloting and aiming skill as well as purchased ship upgrades.

The economy of Elite is largely static. The market within a given system will have only small fluctuations in the prices on most goods as well as availability of said goods, and these prices do not change depending on quantities of goods imported by the player from elsewhere. Prices and availability are instead determined on whether the system (one planet per system) is an agricultural or more industrial one. I have read that this is not the case in Eve, though I fail to understand the details of its system.