SAN FRANCISCO — As the sequel to their blockbuster patent trial nears, Apple and Samsung are miles apart, even when it comes to the value of software patents.

Apple Inc. is expected to tell jurors when the latest trial kicks off in San Jose this week that Samsung Electronics Co. should pay about $2 billion for infringing its patented smartphone and tablet technology. Samsung will counter that Apple’s patents aren’t worth nearly that much—and neither are its own. The South Korean company is demanding only about $7 million for the pair of patents it accuses Apple of infringing.