Do you have a composite index or separate indexes?
If it is a composite index of id and a columns,
In 2nd update statement the a column's index would not be used. The reason is that only the left most prefix indexes are used (unless if a is the PRIMARY KEY)
So if you want the a column's index to be used, you need in include id in your WHERE clause as well, with id first then a.
Also it depends on what storage engine you are using since MySQL does indexes at the engine level, not server.
You can try this:
UPDATE table SET field = value WHERE id IN (...) AND a IS NULL LIMIT 10;
By doing this id is in the left most index followed by a
Also from your comments, the lookups are much faster because if you are using InnoDB, updating columns would mean that the InnoDB storage engine would have to move indexes to a different page node, or have to split a page if the page is already full, since InnoDB stores indexes in sequential order. This process is VERY slow and expensive, and gets even slower if your indexes are fragmented, or if your table is very big
UPDATE table SET field = value WHERE id IN (SELECT id FROM table WHERE a IS NULL LIMIT 10);perform