These are two different but related concepts.

WGS (these days usually WGS84, but there were also WGS72, WGS66, and WGS60, and WGS84 is currently on its 5th revision/update) is a datum and ellipsoid that model the Earth. The ellipsoid used is its own, but it is so close to the GRS80 ellipsoid that it makes no practical difference. The datum provides the following information:

• Where is the center of the Earth, which is the origin of the reference system (co-ordinate system) that you use for locating everything?
• What is the orientation of the spin axis, and hence where is the equatorial plane (for determining latitudes)?
• Where is the reference meridian (for determining longitudes)?
• What is the rotation rate of the Earth?
• What are the basic gravitational parameters for the Earth?
• What are the units of measurement for this model of the Earth?

That’s basically what a datum is (and does), and all datums have to do this. WGS84 does a bit more than that, but it sets the foundation for a global reference frame that links everything.

As an aside, it’s also the reference frame used for GPS, and it is directly connected to the various ITRF (International Terrestrial Reference Frame) instantiations.

UTM is a map projection system: Universal Transverse Mercator. A map projection allows you to take any latitude/longitude based location on the Earth and transform it into an E/N (or X/Y) location on a plane cartesian system. It also works in reverse. UTM can be used with any datum, so it doesn’t give consistent results across datums, meaning the datum must be specified.

Being a conformal mapping system, UTM allows you to use cartesian computation methods on the E/N co-ordinates and your measurements (corrected to allow for the projection distortion), rather than having to do full geodetic calculations for every point and line. In other words, it makes life dramatically simpler for a huge range of surveying and mapping tasks.

In GIS, specifying WGS84 as the datum means you can use GPS data directly. It primarily allows a definition of what you mean by the co-ordinate origin and the orientation of the axes of the reference frame, together with the reference ellipsoid you are using.

Using UTM specifies how lat/long locations are represented as E/N co-ordinates in the database and also on the screen or a printed map.

If you want to use anything other than latitude/longitude to specify locations, you need a map projection. UTM is common for larger GIS projects. WGS84 allows you to have a datum, in the full meaning of the term, and this is projected using the map projection.