Usually, semi-open refers to an adoption in which the adopters and birthparents meet once or twice and on a first-name-only basis. In addition, they may agree to exchange pictures and letters on an annual or fairly infrequent basis through the adoption arranger. (If your adoption arranger advocates a semi-open adoption, be sure to ask for an exact definition of her terms.)
Semi-open adoption is the practice in which information, generally non-identifying, is shared between adoptive families and birthmothers. Usually semi-open adoption consists of the exchange of letters, photos, and emails, either directly or through a third party. It is not unheard of to have some pre-birth, face-to-face meetings or for the birthparents and adoptive parents to spend time together at the hospital during and after the birth.
Closed adoption, not to be confused with sealed records, is an adoption in which the adoptive family and the birthmother never meet and know nothing or very little about one another. With the advent of open adoption, closed adoptions have become the exception in domestic adoption rather than the rule. The term closed adoption is most often used in relation to post-adoption contact, whereas the term sealed records is related to the access of legal documentation surrounding the birth and placement of the adopted child once the adoption is final. It is entirely possible to have a closed adoption and unsealed records or an open adoption with sealed records. The two practices are not mutually exclusive.