I have always been a person who loves to relate topics, and for me, real-life examples play a vital role in understanding concepts that just stay with me for a lifetime.
Waterfall project management is nothing but Buffet and Agile product management is Ala Carte.
In a buffet, the menu is fixed, the cost is fixed and served at a fixed time slot. Similarly, in waterfall project management the budget, scope, and time are fixed and cannot be changed after the project starts. If anything needs to be changed it has to go through the complete cycle and again the 3 parameters are recalculated and fixed.
In the buffet, you get a variety of items in the fixed amount. Most of them you try but just because you have paid for it. There are quite a few which you don't taste and if you are on a diet you have wasted the funds. It's fun for team parties, less coordination more variety, and most of us are happy. Once in awhile buffet for a change is good.
Ala Carte is like you come at any point in time when the restaurant opens, order what you want to eat and pay for what you have ordered. Nothing more and nothing less. If you love the taste and ambiance you can order more and decide to stay longer. The best part is you can even eat with a low budget. You can eat like a king if you have the capacity and budget. As a customer, you get to decide what, when, and how much to eat. You can change your mind and decide to stop after the starters are served, you can eat up to the desserts or you can just have the desserts.
Ala Carte is nothing but how agile works. Change is good, You keep on ordering as time passes you can decide about your food course gradually. Feedback can be shared like I loved the drink but can you add more ice to it or make the next dish a bit spicy. There is more interaction and collaboration between the customer and the captain or the person who attends the table, (s)he shares their inputs even recommends the best dishes.
This is a well-known diagram were in the first figure you find rigidly fixed boundaries that connect the 3 parameters. The second figure is a reverse triangle where budget and time depend on the scope. The scope is kept open-ended and can be changed. This change in the scope will then decide the budget and time. Nothing is fixed, it's variable and allowed to change as more information surfaces and decisions can be made when required. You do not have to plan everything ahead of time. The plan will gradually evolve based on the feedback, market condition, ROI and so many factors.