A kinase adds a group on to another molecule.  A phosphate kinase is usually an enzyme that puts a phosphate group on something.  In this case, the enzyme is putting a phosphate on NMP (Nucleoside MonoPhosphate) or NDK (Nucleoside DiPhosphate).

The nucleoside diphosphate kinases and the nucleoside monophosphate kinases are named for the substrate to which they are adding a phosphate.  .   Nucleoside monophosphokinase refers to adding a Pi to NMP and nucleoside diphosphate kinases refers to adding a Pi to NDP.

Keep in mind that most of the energy in your body is produced as ATP by the electron transport system so the reaction is usually (except for muscle) going from left to right.  That is, using up ATP to produce nucleoside diphosphate or nucleoside triphosphate .

Examples:

ATP + UMP = ADP + UDP The reaction is catalyzed by a nucleoside monophosphate kinase.
ATP + UDP = ADP + UTP The reactions is catalyze by a nucleoside diphosphate kinase.
GTP + CMP = GDP + CDP The reaction is catalyzed by a nucleoside monophosphate kinase.
GTP + CDP = GDP + CTP The reactions is catalyze by a nucleoside diphosphate kinase.
ATP + AMP = 2 ADP The reaction is catalyzed by a nucleoside monophosphate kinase commonly called adenylate kinase or, in muscle, myokinase.

            
When a muscle cell is working very hard, it produces a lot of ADP from ATP. Thus, the ATP concentration drops and the ADP concentration raises. Some of the ADP produced is used to produce more ATP and AMP. This provides additional
ATP for muscle contraction. The reaction is the reverse of the myokinase reaction shown above. Despite this, the enzyme is still classified as a nucleoside monophosphate kinase.