I would argue Agile (in my case agile scrum) is actually deferred planning compared to waterfall. The difference is agile planning I personally feel is your large scale plan is fuzzy / not detailed yet, but your short term plan is planned to extreme detail. As apposed to Waterfall where traditionally you planned the entire project up front (to the extent you could realistically do so)
Agile itself can be broken up into tons of sub methodologies, but at the highest level it's having detailed plans for short time spans 1 week to 1 month, past that is really pushing it. Your longer term plans more than 1 month down the road typically are not planned into much detail (yet) and live as list of features, bugs, etc to be done some day in your backlog.
The planning of your short term "sprint" is very detailed. You plan out the entire sprint, who will do what, technical details, etc. The precision of these plans vary team to team, but generally speaking successful shops tend to air on the side of more planning than less. The end of your sprint is your deadline, all work listed should be done by then (exceptions apply)
Typically you list all your want / need to haves in a backlog, each sprint you start at the most important items divvy them out you your team until you've assigned to the point they'll be kept busy, while still realistically finishing on time.
You repeat this process every sprint. This makes planning progressive so as the situation of the project changes the project can adapt.
Traditionally waterfall you planned everything up front and spent 3,6, or 12 months pounding it all out, Then going back and adjusting things at the end.
one way to think of agile is it's still waterfall, only your releases are weekly not annually. (someone will not be happy I said that, my point is you still plan things through just the scale of the plan is WAY smaller, but more often.)