What is a triglyceride?
There is some minor argument as far as nomenclature goes for these lipids. Most sources I can find, including IUPAC have glycerides as only including esters of glycerol with fatty acids. Monoglycerides have a single fatty acid ester with two free OH groups, diglycerides have two fatty acid esters, and triglycerides have three. Phosphoglycerides are defined separately as esterified derivatives of phosphatidic acids, so you can think of them like glycerides where for one of the substituents, instead of a fatty acid, some derivative of phosphoric acid is present. However, the way the two terms are defined, they don't encompass any common molecules, i.e. there are no molecules that are both glycerides and phosphoglicerides and neither group is a subset of the other.

So: mono-, di-, and triglycerides are subsets of glycerides while phosphoglycerides are a different group altogether, though structurally similar.