If both resolutions were essentially the same, why did the US propose one and then abstain from the other? The intricate wording of these resolutions is actually extremely important, with deliberate choices made down to the letter. For example, the US resolution stated the "imperative of" but did not "demand" an immediate ceasefire; it's like a fucking land acknowledgement with how pathetic it is. The only reason the US proposed their resolution was as a last-ditch effort to dilute the demands of the international community as a ceasefire resolution became inevitable.

Regarding their vote, China's Ambassador Zhang Jun stated that the US resolution set up preconditions for a ceasefire ("supports ongoing diplomatic efforts to secure a ceasefire" "in connection with" the release of all remaining hostages), making it unacceptable, whereas the new resolution "demands an immediate ceasefire" "and also" "demands the immediate [...] release of all hostages," and so makes these matters independent demands without preconditions.

Wrt to the invasion of Rafah, the US proposed resolution specifically notes the inevitability of "ongoing and future operations," noting only the importance of "measures to reduce civilian harm" thereof—this is the "effective green light" Russian Ambassador Vassily Nebenzia was referring to, and further:

One of the earlier iterations of the draft resolution currently in blue said that the Council determined that “under current circumstances a major ground offensive into Rafah would result in further harm to civilians and their further displacement including potentially into neighbouring countries” and underscored that “such a major ground offensive should not proceed under current circumstances”.

This language was apparently challenged by a majority of Council members out of concern that it could be interpreted as the Security Council indirectly approving an offensive in Rafah under some circumstances. In an apparent attempt to address these concerns, in the third revised draft the US moved the language on the offensive from the operative section of the resolution to its preamble and removed text saying that an offensive “should not proceed under the current circumstances”, leaving text saying that “under current circumstances” an offensive would result in further harm and displacement of civilians. It seems, however, that many members were still uncomfortable with the reference to "under current circumstances."

As Yogthos said, do read the the actual resolutions before commenting. The US "resolution" did not demand preventing an invasion of Rafah like the other resolutions had, nor did it explicitly demand a ceasefire like, again, the other resolutions had. It only really demanded the hostages back.

Veto'ing it for "political" reasons like you claim would've been the dumbest thing a state could do seeing how western news outlets have excitedly been using it to portray China and Russia in a bad light. Judging by this thread alone, that seems to have successfully fooled at least 1 person.