Unfortunately, the doc seems to be missing some explanations, and we'll try to update it with Matt's explanations. Thanks for asking about it. The links that Matt posted are the current doc pages that explain these default start rules.
First, I'd like to say that start rules and attributes are different. Lot, LotInner, and LotCorner are start rules. They define which rule to start with in the code (in the rule file that is assigned to the shape). Attributes are not really part of this discussion. They are like parameters that describe properties that a user can change, and they can appear in the code with the keyword attr in front.
Default start rules are automatically assigned to shapes that are dynamically created by street networks. The default start rule Lot is also automatically assigned to shapes from Get Map Data, as you've noticed. Lot, LotInner, and LotCorner are default start rules that are automatically assigned to shapes generated by blocks. Street, Sidewalk, Joint, Crossing, Junction, Freeway, FreewayEntry, Roundabout, and RoundaboutIsland are default start rules that are automatically assigned to street shapes (the first link in Matt's post). I think there are just these two sets of default start rules. The street shapes doc page explains one set, and I think the doc is currently missing some explanation about the other set (Lot, LotInner, LotCorner).
These default start rules are automatically assigned to shapes when the street network is created or when the shapes are downloaded using Get Map Data, but these rule assignments can be easily changed in the Inspector. These names can also be used on any shape. They are not protected keywords that users should avoid using. You can assign the start rule name Lot or LotInner to any shape you want. This just means that the shape will look for a rule called Lot or LotInner in the code, and it will start executing the code with that start rule.
Then, the keywords street.front, street.back, street.left, street.right are selectors that can only be used in certain contexts such as in the setback operation or the comp operation. For example, this allows you to create a setback on a certain side of the lot (e.g. to create a front yard).
setback Operation
Component Split Operation