The first definition is a definition of linkage as in "linkage disequilibrium" - that one has nothing to do with sex linkage.
Sex linked means that the gene or genes involved in a trait are inherited on one of the sex chromosomes (X or Y) and that, as a result, the disease may occur at different rates in different sexes. A good example of this is color blindness caused by a recessive genetic variant found on the X chromosome. Men only have one X chromosome, so if they inherit the variant, they will be colorblind. Women have two X chromosomes, so they will not be colorblind unless both of their X chromosomes have this problem.
In addition to saying "sex-linked", you can also be more specific and say that color-blindness is "X-linked". There are also Y-linked disorders, although they are much rarer since they usually cause infertility and don't get passed on. The term "sex-linked" seems to be gradually dying off as people adopt these more specific terms.
There are also some other terms you may come across, which sound similar but mean different things:
Sex-limited trait: This has nothing to do with genetics and instead refers to whether a person is biologically capable of manifesting a disease. For example, prostate cancer would be sex-limited because only men have prostates.
Sex-influenced trait: A genetically-influenced trait where, although the genes influencing the trait are not on a sex chromosome, a person's sex may still influence whether/how a trait manifests. An example of this would be breast cancer - certain variations in the BRCA genes increase risk of breast cancer in both women and men, but women with a BRCA mutation are still much more likely to get breast cancer then men with a BRCA mutation are.
Unfortunately, some people use the term "sex-linked" to refer to sex-limited or sex-influenced traits, which can make things very confusing.
To read more about these three categories, see: http://www.eplantscience.com/index/genetics/sex_linked_sex_influenced_and_sex_limited_traits/sex_linked_sex_influenced_and_sex_limited_traits.php