Seeing as this hasn't been answered, I'll give some brief and simple info.
2D radar: typically only provide information on range and azimuth of a target. Generally obsolete and not present on most modern ships and aircraft.
3D radar: provides information on altitude, in addition as well as range and azimuth. Prior to development of 3D radars, 2D radars needed to be complemented by a dedicated height finding radar to determine a target's altitude.
Air search radar: radar optimized for searching the air for targets and conducting any cuing or other missions relevant to the air.
Surface search radar: radar optimized for searching the surface for targets and conducting any cuing or other missions relevant to the surface.
Air/surface search radar: radar which can perform both air and surface search roles. Many modern radars (called multifunction radars, for naval ships) can perform multiple roles beyond only air and surface search as well, including fire control for guns, terminal missiles, midcourse guidance for missiles, among others.
VHF: very high frequency, which is a frequency/band that radars can be designed operate in. Other bands include L band, S band, X band. A single radar system is typically designed to operate only in one band. different bands have different characteristics against different kinds of targets, ranges and resolutions and thus have different uses, therefore a naval ship may have multiple sets of radars optimized for different missions.
APAR: active phased array radar, also called AESA (active electronically scanned array). APARs are a type of phased array radar, and are a fairly recent type of radar that only began equipping naval surface combatants in the early to mid 2000s, and are arguably the cutting edge of what naval surface combatants can field as their primary active sensor. Many APARs aboard naval ships are multifunction radars by virtue of their design.
[052C and 052D have the Type 346 and Type 346A APAR on their superstructures, and the systems are both thought to operate in the S band. AN/SPY-1 of Aegis cruisers and destroyers are older passive phased array radars which operate in S band as well. AN/SPY-6 which will be mounted on the Flight III Burke will be an S band APAR like Type 346/A. Type 346/A, AN/SPY-1, AN/SPY-6 are all of course multi function radars, but it is important to note that obviously there can be differing degrees of performance for radars in any category whether they are APAR type or multi function type]
