Electrochemistry can be broadly defined as the study of charge-transfer phenomena. As such, the field of electrochemistry includes a wide range of different chemical and physical phenomena. These areas include (but are not limited to): battery chemistry, photosynthesis, ion-selective electrodes, coulometry, and many biochemical processes. Although wide ranging, electrochemistry has found many practical applications in analytical measurements.
A good working definition of the field of electroanalytical chemistry would be that it is the field of electrochemistry that utilizes the relationship between chemical phenomena which involve charge transfer (e.g. redox reactions, ion separation, etc.) and the electrical properties that accompany these phenomena for some analytical determination. This relationship is further broken down into fields based on the type of measurement that is made.
Potentiometry involves the measurement of potential for quantitative analysis, and electrolytic electrochemical phenomena involve the application of a potential or current to drive a chemical phenomenon, resulting in some measurable signal which may be used in an analytical determination.