Does the legend rule apply to planeswalkers with the same planeswalker type?

As of the July 2018 rules update, the old 'planeswalker uniqueness rule' was removed entirely. Planeswalkers are now subject to the same Legend Rule (CR 704.5j) that applies to legendary permanents — but only if two or more planeswalkers controlled by the same player share the exact same name, not merely the same planeswalker type (subtype).

This means you can, for example, control both Jace, the Mind Sculptor and Jace, Architect of Thought at the same time with no problem, because they are different cards with different names. They both have the planeswalker type 'Jace', but that is irrelevant under current rules (CR 306.4 no longer restricts by subtype).

However, if you control two copies of the exact same planeswalker card — say, two copies of Liliana of the Veil — the Legend Rule triggers. As a state-based action, you choose one to keep and put the rest into the graveyard (CR 704.5j).

Concrete example: You control Chandra, Torch of Defiance and your opponent uses a copy effect so you also get Chandra, Pyromaster. Both are legendary planeswalkers with the type 'Chandra', but their names differ — both remain on the battlefield under your control with no issue.

In summary: same planeswalker type alone is irrelevant. Only identical names on legendary permanents trigger the Legend Rule under CR 704.5j.