The "Total Ion Current" normalization tells Skyline to divide the observed peak areas by the area under the TIC chromatogram that was collected by the mass spectrometer. Some mass spectrometers (e.g. triple quadrupoles) do not record the TIC chromatogram, in which case you would not see any results.
Skyline is supposed to be smart and notice whether your replicates have a Total Ion Current Area value, and, if not, then you should not be offered Total Ion Current as a normalization method, but there are some cases (such as if you have zero replicates in your document) where you are able to choose Total Ion Current even though it is not going to work for you.
MSstats offers Quantile normalization, but Skyline does not offer that as an option. Quantile Normalization works by making it so that, for instance, the 95% most abundant peptide in each replicate will have the same normalized area.
You might learn more about normalization methods if you look at the Absolute Quantification tutorial: