The two largest categories of form are core sections and auxiliary sections. This particular dichotomy was introduced by Jay Summach in his dissertation "Form in Top 20 Rock Music, 1955-89" (Yale University). Summach's work was dedicated to "Rock Music" in particular, but my approach is broader and does not focus on a specific genre or time period. Instead, it can be applied to any music that an analyst believes they hear identifiable groups.
Core sections typically introduce and repeat a work's primary musical ideas and you can think of them as the sections of music that you might sing for someone, if they asked you how the work "went." You can also consider core sections to contain the work's "themes" though usage of that word tends to range from very broad to incredibly specific. Core sections also tend to repeat which is another reason they will often make a stronger impression on your memory.
Main sections are typically the first section that presents primary musical ideas, they are usually repeated later in the work, and are characterized by a relative sense of stability. They are the sections that most would primarily associate most with a work and are typically a key component of the work's identity. The terms for main sections change depending upon the conventions of the genre and form (if it is a form with a name). When thinking about form in general, the main section should be called A, but within a known form it may go by many names including (but not limited to:
Contrasting sections tend to have a broader range of affects and levels of stability. In some cases, they could be indistinguishable from sounding like a main section but they simply were not the first core section and in other cases they may be the most unstable section of the work. Unstable sections may also share many musical features with connective auxiliary sections but the difference is one of being considered a core section or not. Relatively speaking, contrasting sections sound like a primary place in the work, whereas connective sections sound like a place between two core sections. In some cases this line may very well may be blurry but the conventions of a named form can be called upon or employing multiple formal descriptors (e.g., becomes) can aid in providing a classification that feels accurate and not forced.
A stable contrasting section would typically sound normal if it started the work instead of the main section, its ordering is the only reason it is considered contrasting. It simply contrasts with the work's main section. On the other hand, the instability of an unstable contrasting section would likely sound unusual at the start of a work simply because it is statistically common for work to start with a stable section.
When thinking about form in general, contrasting sections start with the letter B and each, subsequent new section receives the next letter in the alphabet (C, D, E, etc.). Within a known form, contrasting sections go by many names including by not limited to: