The block schedule usually refers to one where you take a full course in half a year (much like you would in college.) There are typically two “terms” for academic classes. (There may be a short one – like a college Jan plan – in addition.)
The modular schedule rotates the courses in throughout the year over 7 marking periods. So unlike the block schedule, where you would take French 1 from September though December, you would have the course in 3 parts over the year – maybe October, Jan, and April. From what I have read about it, the numerous “fresh starts” during the year is energizing. The brief review at the beginning of the continuation reinforces learning. And the courses can be completed before AP and IB exams. It also makes some doubling up possible, so a kid could do French 1 and 2 in one year (assuming mods lined up that way.)
It must be a scheduling nightmare! But it also allows kids to drop into a class at an appropriate point. Maybe a kid who has done some programming would start that class in the second mod.
It also allows short courses and/or travel study.
Edited to add that George is currently using the same schedule you described for Madeira. Kids are liking it but it still means they are taking 8 classes at a time, even though only 4 meet each day. With a mod schedule, they would have those same 4 every day for however many weeks. Then a different 4 in the next of the 7 “terms”.