Specification. Tesla published a specification. It can't publish a standard, since it isn't a standards body. J3400 will be the standard based on the specification published by Tesla after checking and possible refinements. Nitpicky, yes, but also not. Since standardization includes stuff like governance agreements, governance organization, Patent and IP licensing clearance and so on. The technical spec is only part and maybe simplest part of the standard. The really important part is the legal and contractual matter, so that when standards body does officially adopt standard everyone can use it with confidence of knowing under what terms and payment said standard is offered and that there will be no lawsuits waiting to jump out in the bushes.

Also theoretically there can be technical differences between J3400 and Tesla connector, if those changes are done in backwards compatible fashion to Tesla's earlier plug. Not out of having to, but out of it being desired feature for utilization of existing infrastructure.

Whole point of J3400 is it isn't the "Tesla plug" anymore, it is a plug governed by Society of Automotive Engineers. It just happened to originate from specification developed by Tesla originally.

Just like how the European Type 2 plug is sometimes called Mennekes, since Mennekes Elektrotechnik GmbH & Co. KG was the original designer. However officially and governance wise it is now the Type 2. It is governed by IEC, not by Mennekes anymore.