Besides the fact that a mohel is performing the bris in order to bring the baby into the covenant, and must handle it as a religious ritual, there are also differences in the medical procedure. The minimum amount required for a bris is more than that required for a surgical circumcision. There are also problems involved with the clamps that surgeons use. A "bloodless" circumcision is not allowed for a bris. Also there are discussions as to what clamps
are allowed or forbidden for a bris, and specifically how to use them in appropriate ways.
Jewish Ritual Circumcision
A mohel’s technique is different from a surgeon’s: Clamps are
forbidden; instead a butterfly-shaped shield protects the glans while
the mohel removes the foreskin with a sharp scalpel. (In a bris, all
membrane below the corona of the penis must be removed, which is not
necessary in a medical circumcision.)
Brit Milah
Milah in a forbidden fashion
We should begin by noting that milah comprises two elements: milah and
priah. Milah is the removal of the orlah (the foreskin), and priah is
the removal of the thin membrane which covers the flesh underneath.
The Shulchan Aruch rules, in accordance with the Gemara:
“If milah was performed but not priah, it is as if milah was not
performed.”
The Rishonim and Achronim, in turn, wonder if milah and priah may be
performed “as one”. In other words, may the mohel – either by hand or
with a special instrument – hold the two skins together and cut them
simultaneously? Many poskim are stringent in this regard, and most
contemporary authorities hold that, l’chatchilah, milah and priah
should be performed separately. However, Rav Moshe Feinstein zt”l
disagreed, and many mohalim rely on his opinion. (A related question
is whether or not the mohel may wear gloves during the milah.)
Nonetheless, there are a number of instruments which definitely
invalidate the milah. For example, the so-called “clamp” essentially
kills the orlah before the cut, and hence, no blood is involved. But
the dambrit (the blood of the brit milah) is one of the main
components of the brit, and therefore, mohalim may not use this
instrument. Interestingly, several studies have shown that the baby
endures more pain with this type of instrument. In any event, when
such an instrument is used, the brachah is abrachah l’vatalah (“a
wasted brachah”).
Note that there are discussions as to what a clamp
means, what kinds of clamp
are forbidden and what is allowed. This is only the most general statement. See Contemporary Brit Milah Issues for one such discussion.
Note that even if the child has been circumcised and sufficient skin removed to make it a kosher bris (something that is not guaranteed) a drop of blood must be taken as part of the bris. Adult males or older children who convert or who had lived in circumstances where it could not be done (such as the former Soviet Union) but had been circumcised can be examples of this. If an adult must have a full bris (something that is being done more and more according to various articles) then a specially trained surgical mohel must be consulted.
The Objective of the Ritual Circumcision
For this reason a person who underwent a medical circumcision, without
intent to fulfill this commandment, should undergo a subsequent
procedure performed with specific intent to fulfill this mitzvah. This
subsequent procedure is relatively painless, involving only the
drawing of blood from the reproductive organ, but done in the name of
Brit Milah.
For further details, check with a mohel. You should also note that many times a mohel will be used even for a circumcision because of his expertise and the number of procedures that he has done compared to a regular surgeon.
Methods of Circumcision goes into gory detail on the medical procedures involved and the difference from a bris. It is too long to quote here but can be read at the link.
Why a Kosher Mohel?
A Mohel performs a Brit using a Magen shield, and a Izmil (scalpel),
which severs the skin safely, quickly, and efficiently --- within
fifteen seconds, resulting in a minimum of pain. Doctors use a clamp,
which takes several minutes, causes unnecessary pain, and can have
serious health consequences. A letter from the Food and Drug
Administration (FDA) issued in August of 2000 states,
“...although research suggests that circumcision is generally a safe
procedure, we are concerned that some device-related complications
have occurred. We have received 105 reports of injuries involving
circumcision clamps between July, 1996 and January, 2000. These have
included laceration, hemorrhage, penile amputation, and urethral
damage.”
Note that it is precisely the clamps to which the FDA objects -- We at
Brit Yosef Yitzchak couldn't agree more. Not only does the clamp not
conform to the strictures of Jewish law, but it really isn't safe for
any type of circumcision.
HATAFAT DAM BRIT FOR CONVERSION discusses what is done when a circumcision has been done but not a bris.
Brit Milah for an Adult discusses how uncircumcised adults can get a bris in Eretz Yisrael.