Hi Eugenia, I see this question is a few months old, so you may already have figured it out. Nonetheless, here is some clarification. The word “will” has many different connotations (implied meaning) in many different contexts just based on how it is used and the tone, which is the hard part for non-native speakers. Since you are clear on the first part, I will address the second. I assume what they mean by spontaneous plans is when we are discussing who in a group will do something. In that case, it’s not so much about the individual’s certainty (if I’m understanding the context correctly) but about the uncertainty of the group as to who will do something. “Who’s going to go get the pizza?” “I will do it.” You would use it to volunteer to do something. “Will” and “going to” aren’t interchangeable in this context. Also, a note. In most cases, native speakers would not say “I will do it” in this example. Conversationally, it would generally be contracted to “I’ll do it” (I’ll go get the pizza). To complicate it even more, if you asked the same question “Who’s going to get the pizza?” and it had already been decided, the person responding in that context would say “I’m going to get it” not “I will get it” because they are not volunteering to do the task but letting you know that they are the one in the group who is doing it. I used pizza because your baby example would have many more layers to it. As I struggle with Spanish having 5 billion verb conjugations, I sometimes wonder why they say English is so hard to learn. This example reminds me. Hope this helps!