I'm not able to explain how the individual regex variants behave, but you may well be right in that they apply varying levels of optimisation.
Basically what happens is that both patterns force the first work to be anchored in some way at both ends. The initial '\b' means that the match must begin at a work boundary - either the beginning or end of a work. Therefore the only possible places where a match can start within "mycar car" is with the first character "m", the first "r" before the space, the "c" of the 2nd word and the last "r" in the string.
The next pattern operator is a '\w' which means that there are only 2 places where a match can start - the "m" of "mycar" and the "c" of "car".
Taking the first of these, both regex patterns will initially match the same characters because the '\w+' will match all of "mycar" and stop before the space and this is the captured text. Because there is a space character in the pattern, the additional '\b' in the second pattern is not really relevant.
Both patterns will then match the space and try to match the captured text and both fail.
Both pattern will then try to backtrack by releasing the last character captured in group #1 - this is the "r" but both will immediately fail, the first because it requires a space character to be matched next (and the "r" is not a space) and the second because it requires a word boundary but has the "a" before it and the "r" after it. Both will continue to backtrack until all of the matched characters are returned and the pattern as a whole fails.
I'm not sure how you have determined how each pattern is actually processed but, as far as I can see, both should be almost identical unless the regex engine is applying some optimisation such as "knowing" that any character captured by the '\w+' and released by the backtracking cannot then form a word boundary (which by definition is either the point between '\W\w' or '\w\W') and so skips the intermediate attempts.
Also, what is your purpose in analysing this? The patterns (to me) seem to be too similar to see any differences, especially as you seem to be using the same regex variant?
Susan