Custard should taste eggy. This is a feature, not a bug. However, from your mention of flour, I think what you're talking about is a souffle, not something like a creme brulee or along those lines. Would that be correct?
Edited based on subsequent clarifications:
Ah. Your method is sorely lacking, and your ingredients are off. You need to temper the yolks first, you need to use yolks only, and use cream instead of milk. Here is a smaller version of what I use at work for creme brulee:
- 1L 35% cream
- 11 egg yolks
- 1C sugar
- 1 vanilla bean, scraped
Bring cream to a simmer with the vanilla seeds and pod (you can use approx 1.5tsp vanilla extract, pure not artificial, instead). While it is heating, beat the yolks and sugar together until just incorporated. Pour the cream into the eggs whisking briskly to prevent curdling. Pour mixture through a fine chinois. Skim off foam, pour into ramekins. Place ramekins in a pan, add water to 1/2way up the sides. Cover pan with foil. Bake at 275 (convection) or 325 (non convection) for approx 40 minutes, until wobbly in the centre but set. Chill until set, eat.
The deflation is caused by a souffle effect coming from including the egg whites, which are never used in a custard--custards, creme anglaise, etc, are always yolks only. When you include the whites, air will be trapped inside temporarily, and will escape/collapse when the mixture cools. If you bake until fully stiff with my method, you will get hard and rubbery custard by the time it is set in the fridge.
Also, save the whites--they freeze well--for meringues or souffles.
A very common type of pudding is a pudding made from liquid thickened with starch. It is usually made with milk, but you can use other liquids as you see fit. Fruit juice will probably work best. For starch, use plain potato, corn or wheat starch. The "absolutely no fat" condition is very detrimental to the taste. A trick to make it taste richer would be to include some whey powder. Any sweetener will work - sugar, baking sweeteners like honey or agave syrup, or artificial sweeteners (keep in mind the max temp for artificials). You can enhance the flavor wit the usual suspects - vanila, cinnamon and other spices - and/or serve with syrup poured over. Adding food coloring is also a good option, as it affects the perceived taste too.
To prepare the pudding, use a base ratio of 1 part starch to 10 parts liquid (you can change that later, depending on your preference for firmness). Mix the dry ingredients (sugar, cinnamon) with the starch in a small bowl. Stir in some cold liquid, around 1 tbsp per 25g starch, until you have a slurry. Bring the remaining liquid to a boil. Remove from the heat and quickly stir in the slurry. Return to the (reduced) heat and let simmer for some minutes, stirring contantly. Stir in the liquid ingredients (e. g. honey, molten caramel). Pour into the form(s) and leave it to cool, at best overnight. It will set and should be firm enough to slice. Alternatively, it can be eaten warm (and still soft) from bowls.
You mention Jello. I don't consider gelatine jellies to be a "pudding", but maybe this is a language problem on my part. You can make a gelatine "pudding" with powdered gelatine, just follow the instructions on the package. Gelatine itself is pure protein and does not contain fat.
It is also possible to use modern thickening agents to thicken a juice or another liquid to a more or less pudding-like consistency, but this is unusual in home cooking. If you are interested, look up guar gum or xanthan gum. There is a free e-book oh hydrocolloids often linked here on SA, but it probably goes much beyond what you need. Still, you can search for it if interested.
Best Answer
Sometimes it is, sometimes it isn't. Depends on what the manufacturer put inside.
The term "pudding" is somewhat broadly defined. It can include eggs, or starch, or both, or even be applied to kinds of dessert which are not made from thickened milk. "Custard" is somewhat more specific, I would insist that a custard is always egg thickened, and that the most typical custard is yolk thickened - but it can include starch sometimes.
Manufacturers of powders who write "pudding" will almost always use starch (although sometimes they use modified starch, which ends up tasting differently than homemade pudding), and sometimes also powdered egg. Manufacturers of powders with the label "custard" might use pure egg powder, or a combination of a starch and egg, but they could also just decide to label it "custard" even if it doesn't include egg.
So, I would expect that they are in principle different, because a "pudding" sachet is very likely to contain starch and no egg, and a "custard" sachet is very likely to contain an egg, and no starch, or little starch. But due to inconsistent labelling, if you just grab a package of each from a random brand, you can end up with the opposite case, or with two packages containing the same thickener.