Why is iso-octane different from other iso-s? While learning nomenclature of organic compounds I found the common  names to be a bit difficult to learn than the IUPAC ones. One of these common name stuff is the iso-,neo-, sec-, etc. So I searched for the ways to differentiate between these on the YouTube and found this video (note that the anchor of the video uses hindi for communication so it might not be intelligible to most people here). To summarize what the anchor said:

Prefix-iso: is used when all carbon atoms except one form a continuous chain.
$$\mathcal {OR}$$
They have a structure like this:


Now in the same video the anchor says that iso-octane is an exception to this rule, as it has the following shape:

Before this came in the video I formed the view that these are just the ways of naming compounds with similar structure but now I think that that isn't the case. So:

Why iso-octane has shape different than the other iso-s?

The anchor says that the structure of iso-octane was determined experimentally. This implies that there is some way to identify these compounds without knowing their structures beforehand so:

How do we know that whether some given compound is iso-, neo-, etc?

What might be the most general guidance for using iso-, neo-, sec- and tert- prefixes?
The usage of non-standard prefixes such as "iso" has never been defined with hard, unambiguous rules such as those in the IUPAC recommendations. Instead, their usage has often more been "by convention". In Organic Chemistry (1st ed.) by Clayden et al., the authors write (p 315):


  Strictly speaking, if the standard meaning of ‘iso’ is followed, the name isooctane should be reserved for the isomer 2-methylheptane. However, 2,2,4-trimethylpentane is by far the most important isomer of octane and so, historically, it has been assigned this name.


(This phrase is also found at Wikipedia, where it is copied wholesale without any indication that it's a direct quote. Please don't do this in your work. Even if you provide a citation, you should either paraphrase the information, or clearly indicate that it's a quote, e.g. by enclosing it in quotation marks.)