If the subject of your sentence is "I", then Barrie's brief explanation correctly summarizes the essential difference between going to and will. Example:
- I'm going to go shopping after work today.
means that you have already planned what to do later.
- What are you doing after work today? - Haven't thought about it. Maybe I 'll go shopping.
indicates a plan made at the time of speaking.
Of course, you are not always the subject when talking about the future, and the focus may be on predictions rather than plans. In such cases there is no simple rule to follow. For example:
- She's going to have baby (not: She will have a baby)
and
- The baby will be her second child (questionable: The baby is going to be her second child)
Talking about the future is one of the most difficult aspects of English grammar for non-native speakers, and includes many more than the two forms discussed here. I recommend investing in a good reference such as Swan's Practical English Usage, and asking specific questions here on this site if you are not sure which form you need in any given context.
English has no future in the future because English has no future tense at all. English verbs approach tense from two perspectives: before now (past), now and after now (present/nonpast). As such, we can conjugate the verb to eat as follows:
I eat.
I ate.
But there is no way to conjugate the verb for the future, and so we resort to periphrastic constructions to form future aspects, which, for better or for worse, usually infuse other meaning into the sentence:
I will eat (volition).
I shall eat (obligation).
I may eat (possibility/permission).
These all imply future time (and thus form the future aspect), but may infuse undesired meaning into the sentence. Nevertheless, we also have less meaning-rich, albeit more verbose, ways of expressing future time:
I am going to eat.
I am about to eat.
So, although there is no future in the future tense, we can form a future in the future aspect by combining the foregoing constructions:
I will be going to eat.
I will be about to eat.
Both of which sound fine on occasion, but may grate on the ears (eyes) if heard (read) too often, especially in the passive voice: the food will be going to be eaten.
It is also worth noting that the present tense is often used for both present and future time, often making the future aspect seem too verbose where it is still grammatical. Consider the following pairs:
I am going home tomorrow. / I will be going home tomorrow.
He heads out in an hour. / He will head out in an hour.
In each pair, both sentences mean about the same thing and, at least where I live, the average Joe is more likely to say the first. This is merely something to consider, however, and it is not meant to discourage your idea at all.
Best Answer
It's worth noting to begin with, that in a way English has no future tense.*
Its verbs don't have future tense as do those of many other languages, and so all our ways of talking about the future are with combinations of verbs that are either infinitive or in other tenses.
Will/Shall Future
The form you say you learnt in school uses a modal (will or shall) with a bare infinitive; "I will describe other future tense forms in this post"†
Other Modals for the Future
We can use other modal verbs to change attitude or belief: "I might explain it well" refers to the future, but unlike "I will explain it well" it offers a future possibility with less conviction than will.
Sometimes it's not clearly present or future; does "I can stop writing" refer to the present (I have the ability to stop writing right now) or to a possible future? Really, it's both as one entails the other. (If I have the ability to do something, then I might in the future; if I might do something in the future, then I have the ability to do it).
Going to Future
The going to form uses a present tense expression to indicate a future outcome.
Consider the present tense phrase "I am going to the shops". While it describes my present action that moves me through space, there is an entailed future outcome of my being at the shops. Now consider, "I am going to the shops to buy some food". Again this is a present tense statement that moves me through space, but we have more information about the future outcome. Now consider, "I am going to buy some food". Here we've lost the spatial movement, but kept the temporal movement to the future.
Copula-Gerund Future
We can also just use the present tense, and have other statements supply the information that places us in the future. Your example of "I am doing something at 5:00 PM" is an example of that; "I am doing something" is present tense, but the additional "…at 5:00pm" indicates a future time-frame.
Simple-Present for the Future
This also goes for the simple present: "my aunt arrives" is present, but "my aunt arrives tomorrow" makes it work in a future time-frame.
Point of Commencement Future
A variant of this is to combine the present with an expression indicating that we are presently at the point when something is about to happen, which hence must be in the immediate future. "She is about to leave", "He's on the verge of going nuts", "I'm just coming to describing the 'worse is yet to come' form."
Copula-To Future
The is to form uses the present to state a future the present is pregnant with. It's often used for plans "President Obama is to visit Cuba" as in one of the comments above means there is a plan now, for such a visit. It is also used to indicate events in the future that are consequent on conditions now. "Economy to improve" suggests not only will the economy be better in the future, but it will be so because of how things are now. (The is being dropped as is common with headline styles).
Your "the worse is yet to come" example is a case of this; it says things will get worse, but does so based on how things are now.
Note that we might say "the worse was yet to come" as a future-of-the-past sense even if nothing at the time would have made "the worse" inevitable. People tend to talk about the past as if the way the unfolded was destined and inevitable, even if they don't believe in kismet.
It's also worth noting that "The worse is to come yet" is logically as sensible, but "is yet to" is idiomatic.
The word yet means "still, at the present point in time". When we add it to "The worse is to come" it emphasises the now of that to show that because it is now still to come, it is therefore in the future.
"The worse is going to come yet" puts the yet on the future side of the "going to", and yet being about now does not belong in the future.‡
However, "The worse is not going to come yet" works, because it implies a further future (when "the worse" does come), so yet is still referring to a point in time "now" prior to a referred-to future.
*The hedge of "in a way" there is because depends on just what we mean by tense. Sometimes (particularly in teaching contexts) we include aspects as part of tenses, and sometimes we don't. Sometimes we include all constructions that affect time reference, sometimes only morphological changes. In the last case, we would understand English as having only a past and a present (or perhaps, non-past) tense. These different meanings of tense have different value in different cases, but ironically the meaning in which there is no future tense is the most useful for examining how the future tense works.
†There are some who would say that I should use "I shall describe…" above, preferring shall for the first person and will for the others and then reversing that to indicate strong determination or an obligation. Most people though tend to just use them interchangeably, with will being more commonly used. Strictly following the "I shall, you will" rule can work well in formal registers, but by the same token seem stuffy in less formal registers.
‡It's different with "the worse will be yet to come" which refers to the future-of-the-future because while that yet is in the future, it's still in an earlier time-frame than the to come talks about.