Your questions are directionally correct, but need fine tuning.
ESIGN has no implementing regulations. The Fed and other banking agencies are only permitted to interpret ESIGN when necessary to issue and maintain other regulations (such as Regs. E, DD, Z, etc.) As a result, you must look to each of these existing banking regulations for guidance, not to ESIGN.
Your first and most important concern is about the form of disclosures. Reg. E, for example, says that Reg. E's disclosures must be provided "in writing, and in a form the consumer may keep." (Sec. 205.4(a)(1))
Other consumer protection laws and regulations can (and do) have different standards for the "form of disclosures"--you must study all that apply to the products for which you plan to offer e-delivery of documents.
When disclosures must be "in writing", you have two choices: paper and electrons. As a convenience, the consumer protection regulations (Sec. 205.4(a)(1), for example) may alert the reader to ESIGN's procedure for substituting (legally) electrons for paper.
You asked if there is a difference how the account opening disclosures are given. Yes, it matters, but only to a limited extent. Sticking with Reg. E, you can see there are two considerations:
- the method you use must be sufficiently understandable so that customers can navigate your demonstrable consent "test drive", and
- customers must be able to capture and retain (in some manner or other) the content of the disclosures.