I suppose you could say that it’s equivalent to “total utilitarianism that only takes into account the utility of already extant people, and only takes into account their current utility function [at the time the decision is made] and not their future utility function”.
(Under mere “total utilitarianism that only takes into account the utility of already extant people”, the government could wirehead its constituency.)
Yes, this is explicitly inconsistent over time. I actually would argue that the utility function for any group of people will be inconsistent over time (as preferences evolve, new people join, and old people leave) and any decision-making framework needs to be able to handle that inconsistency intelligently. Failure to handle that inconsistency intelligently is what leads to the Repugnant Conclusions.
I think the key difference is that delta utilitarianism handles it better when the group’s utility function changes. For example, if I create a new person and add it to the group, that changes the group’s utility function. Under delta utilitarianism, I explicitly don’t count the preferences of the new person when making that decision. Under total utilitarianism, [most people would say that] I do count the preferences of that new person.