Eh, no again. By one of a legendary, the rules mean one instance of that card, with no other copies, existing on the battlefield under your control. You could only have one
Thassa, God of the Sea in play. A second one enter the battlefield under your control, or acquired from your opponent, would enact the state based effect, requiring you to sacrifice one of them. In the example you originally posted,
Tolarian Academy and
Academy Ruins, you could have both in play at the same time. Under the previous rules, playing a second of either would have destroyed both copies, leaving the other in play. Now, you can still have both in play at the same time, but playing a second of either makes you choose between the two matching cards and sacrifice one of them. It is possible to have multiple legendary creatures, land, artifacts, and enchantments in play at the same time, as long as there doesn't exist two or more of a thing, unless you had a
Mirror Gallery affect occuring.
By type, I was referring to the Planeswalkers of matching Subtype; you can have only one planeswalker of any subtype in play under your control at a time. There are five Planeswalkers that have the Ajani subtype:
Ajani Goldmane,
Ajani Steadfast,
Ajani Vengeant,
Ajani, Caller of the Pride, and Ajani, Mentor of Heros. While you could have several of them in your deck, you can only have one instance of a planeswalker with the Ajani Subtype in play under your control at a time.