Is database record access sequential after retrieving the indexed page from disk?
In SQL Server, for a regular index (i.e. not columnstore or Hekaton) the storage engine can choose one of two methods to find the start or end point of a search. The first option is a binary search using the offset array at the end of the page. The second option is to use linear interpolation.

After the search start/end point is found, any range-scan portion of the search is essentially sequential. More specifically, the engine saves a 'cookie' to remember the search position.

When the next row is needed by the execution engine, the storage engine validates that the cookie is still valid (i.e. a concurrent change hasn't affected the physical structure) and proceeds to find the next matching record from that point, using the offset table and previous/next page links as necessary, searching either forward or backward. If the cookie is invalid, the engine effectively re-seeks to find the correct current position.

A read-ahead mechanism is used to help ensure pages needed by a range scan are present in memory before the page is needed by the execution engine.