"MATCHES" in a predicate does a regular expression match (and "[c]" is for case-insensitivity), so this should be similar to your jQuery code:
NSString *pattern = [NSString stringWithFormat:@".*\\b%@.*", [NSRegularExpression escapedPatternForString:term]];
NSPredicate *predicate = [NSPredicate predicateWithFormat:@"self MATCHES[c] %@", pattern];
NSArray *filteredArray = [possibleTerms filteredArrayUsingPredicate:predicate];
If you want to get all strings in the array that start with the given term, you can use the simpler predicate
NSPredicate *predicate = [NSPredicate predicateWithFormat:@"self BEGINSWITH[c] %@", term];