" A syndrome is a convenient label used for people who show a particular constellation of symptoms. In this case, the underlying genetic cause is seen by medical professionals as equivalent to having the syndrome. It is not possible to have this syndrome's label given to a patient without the underlying genetic abnormalities. However, it is possible to have one or more of the "symptoms" of the syndrome (more about those below) without having KS. Klinefelter's Syndrome is not a disease, you can't catch it, and other family members are usually normal. .
Symptomless Syndrome.
When medical professionals discuss the syndrome, they are usually referring to the classic case, in which there are many clear symptoms. However, this is not the only possibility. The syndrome can be very mild, in which case the person may appear to be 44+XY (normal), or it may be pronounced. Some people have so few symptoms -- usually because treatment was begun at a young age, but sometimes because they have only very mild expression of the KS classic traits -- that they prefer to think of themselves as being genetically different from the norm but without the syndrome. However, as a biologist, I can't agree with this; there are some signs of KS (such as those affecting testicular development), which are universal. Others, such as language processing problems, may be very mild in some men, but will still be present when investigation is done.
One reason for the various expression of KS is that there can be different gene expression in different cells due to mosaicism, or there can be mitigation from other chromosomes. A discussion of mosaicism would be off topic, but to summarize it means that different chromosomes will express in different cells, so that some cells will have a normal XY expression, while others will not. The degree of mosaicism can affect the expression of the syndrome. In addition, the XXY is appearing against a background of the 44 autosomes; this can lead to different degrees of expression, too.