I used to cook plenty of purple sweet potatoes when I was living in africa:) Sounds like you maybe cooked them too long...
They can be extremely tasty, sweet with a "perfumy" hint if you are lucky. They are best boiled with the skin on like you did and peeled afterwards (as the taste is preserved better that way). As for cooking time it really depends on the size (which means the potatoes are likely done at different times) but you can always feel when they are done by pressing on the potato with a fork - it should give slightly/be soft. I think it usually took me about 30min but I didn't use a clock. It may shorten the cooking time slightly to make holes in the potatoes with a fork (this also adds to the "creaminess").
I guess they do sometimes get a softer, more "creamy" consistency than your usual potato when well done. However the taste is richer and in my opinion far superior to orange sweet potato. If you prefer a firmer potato, just let your potatoes stay on the firm side (in my experience, though, the taste is enhanced by letting them go soft). But boiled ones would anyways mainly be for puddings as it gets rather sweet.
For panfrying I would suggest avoiding boiling the sweet pots first. Simply peel/wedge them raw, fry them as chips until done and serve with a spicy/hot dip - yum.
It depends on what you mean by "yam".
Once upon a time, in the deep south of the US, there was a tuber known as the sweet potato, and it was good. And then one particular grower decided to sell theirs under the trade name "yam" to get better marketing recognition. This lead to some folks in the US calling sweet potatoes by the name yam, especially in the context of candied yams (a sweet casserole of spiced sweet potato).
So if the word "yam" is being used to mean a variety of sweet potato, then they are culinary identical. Sweet potatoes of all variety are, well, potato sized (or a bit bigger than the average potato), and their color can range from whitish through yellow, orangish or reddish. Most grocery store varieties are fairly orange in color.
True yams originate from Africa, and are far more starchy and fibrous than sweet potatoes, no matter what they are called, and are used in entirely different ways. They can be very large, football to basketball sized or larger. There are also a tremendous variety of true yams.
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Actually, yams are often white, and may be purple or other colors.. In the US, what we get labeled as yams are actually sweet pototoes. (They were similar to the african yams that people were used to, and the name stuck, sort of like how 'pepper' is used for chilies, but they're not even close to the same thing.)
update A longer explanation of the confusion between yam & sweet potato in the US.