In SuperBPE, a fixed number of tokens are learned, and then the constraints of pretokenization are removed entirely, and then the remainder of the target vocab size is learned.

In Boundless BPE, no schedule must be chosen, because there is not any point at which the constraints of pretokenization are removed entirely. Instead, at any point in the learning process, merges between adjacent pretokens are permitted if the pretokens are each represented by a single token. There are some additional details about how the authors incorporate Picky BPE, which I will not try to repeat because I would probably get them wrong.

Yes, they were concurrent work. (Co-author of BoundlessBPE here). A sibling comment describes the main differences. Our paper motivates why superwords can lead to such a big improvement, by overcoming a limit that pre-tokenization imposes on current tokenization methods. The SuperBPE paper has a wonderful set of downstream evaluation runs. So if you're interested in either, they are quite complimentary papers.