clear meaning of .* in regex

. means match any character in regular expressions. * means zero or more occurrences of the SINGLE regex preceding it. My alphabet.txt contains a line

abcdefghijklmnopqrstuvwxyz

Doesn't grep a.*z alphabet.txt mean match any substrings that start with a, with zero or more occurrences of any type of SINGLE character in between them, and end with z? For example, abz, abbz, ahhhhhz, but not abbdz?

I thought grep a.*z alphabet.txt wouldn't catch the line in my alphabet file.

* means that the immediately-preceding pattern is repeated, not that the matched text is repeated. For example, [ab]* means (|[ab]|[ab][ab]|[ab][ab][ab]|…) The pattern [ab] is repeated zero or more times. It will match "aba" because that properly fulfills the pattern [ab][ab][ab].

With .*, it becomes (|.|..|...|....|…), so it matches any number of characters, and the characters can differ.