The controlling principle is that tokenizing changes the wrapper and not the contents. The Commission states it flatly: "A security is a security regardless of whether it is issued, or otherwise represented, offchain or onchain. All devices and instruments that have the economic characteristics of a security are securities regardless of format or label." That cuts both ways and both are worth holding. Tokenizing a share does not free it from the registration, disclosure and intermediary rules that attach to shares. Equally, tokenizing a commodity does not make it a security. The question is always what the instrument is economically, which is the subject of the security page, not what technology records it.
What a holder actually owns is where the substance is, and it is not guaranteed to be the underlying asset. The Commission is explicit that "there are a variety of models used to tokenize securities, but they may vary in terms of structure and the rights afforded to holders. As such, the rights of a holder of the crypto asset may be materially different from the rights of a holder of the underlying security, including economic and voting rights." So a token described as representing a share may or may not carry the vote, may or may not carry the dividend, and may or may not give the holder any direct claim against the company at all. The release describes a category of digital security that does not convey the same legal rights as its offchain counterpart but instead entitles the holder "to receive economic distributions from a central party" that manages the underlying interest on holders' behalf. That is a materially different position from being on a company's share register, and nothing on the screen distinguishes them.
The split that determines how many things you are exposed to. The Commission separates tokenized securities into two categories: "(1) securities tokenized by or on behalf of the issuers of such securities; and (2) securities tokenized by third parties unaffiliated with the issuers of such securities, which may involve the third party issuing a separate security that derives its value from or is otherwise linked to the subject security." In the first case the token is the issuer's own instrument in a different format. In the second the token is somebody else's instrument that tracks the issuer's, and the holder now has two exposures rather than one: to the underlying asset, and to the third party that promises to hold it and honor the link. Whether the arrangement performs in a stressed market is a question about that third party.
Where this sits among the neighboring terms. The classification of crypto assets into digital commodities, digital collectibles, digital tools, stablecoins and digital securities is set out on the crypto token and altcoin pages, and a digital security is the fifth of those. Two adjacent structures are deliberately not this page's: a receipt issued for a deposited crypto asset on another chain is a wrapped token, and a token designed to hold a fixed value against the dollar is a stablecoin, which the Commission treats as its own category. The footnote to the digital-security definition adds two precisions worth carrying: a non-security crypto asset that is subject to an investment contract "is not a tokenized security", and a stablecoin that does meet the definition of security on its own facts is one.
A last practical point. A tokenized security is still a security, so the ordinary questions about an offering apply to it in full: whether the offering is registered or relies on an exemption, who may buy it, what disclosure the buyer receives, and whether a resale is permitted. Those are the subjects of the private placement and unregistered securities offering pages, and tokenization does not answer any of them.