There seem to be two different teams, or at least... two different distinct styles. The differences between them are mostly the art style and the story and superficial things like that. Every single "Tales of..." game I've played has shared certain similarities. The battle system gets upgraded a little bit as the series goes on, but it's basically recognisable as the same system from the first game they did. There are common elements like Grade, cooking, titles, combos, gels, skits, recurring names for items and equipment, etc.
You'll find each game recognisable, but still distinct in terms of story and setting. There are some exceptions, such as how the two you've played are connected, and there's two games in the Tales of Destiny series, but on the whole, the relationship of one game to another is much like that of Final Fantasy.
I'd say they are ALL worth checking out, although you might not like them all equally. Personally I find Tales of the Abyss, Phantasia and Symphonia to be superior, but then I haven't played all of 'em. I have yet to play one I didn't enjoy.
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The story resemblence between Symphonia and Phantasia is because Symphonia is a preqeul. Other games in the series have separate stories. There is a similar overall format though: real time battles (though the style varies a fair bit), skits, side-quests etc. They are all pretty different though. There is a Tales formula but I don't think it will feel stale from what you have played (you've only played one recent game after all).
Oh, and Nintendo didn't "make" Symphonia. Namco (now Namco-Bandai) made them all (save Tempest IIRC) and Nintendo has nothing to do with any of them, though I heard they funded/organised the translation of Symphonia.
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