Munchausen is when one literally makes themselves ill by injecting poison into themselves, creating/worsening infections, etc. - to seek hospitalization because they want to be taken care of by medical staff. They actually are creating symptoms but are deceptive to staff as to what is going on. They literally do make themselves sick and subject themselves to unnecessary surgeries.

M by proxy is when the parent makes the child sick by numerous methods - such as described above, severely malnourishing the child (to create a baffling "failure to thrive" case). All this is done in secret with the goal of having the child constantly in the doctor, hospital, testing, specialists, having to use medical equipment, etc. It is all being done by the parent because they are seeking attention as the doting, responsible parent and receive a lot of pity.