There are many ways to classify PCB, by conducting layers, toughness, assembly type, base material, special function, wire forming method, with or without core and surface finishing.
You can scroll down to bottom to see the picture of PCB classfication.
By conducting layers, PCB can be classified to single layer PCB, double-sided PCB, multi-layers PCB. Multi-layers PCB can be divided to regular multi-layers PCB and build-up multi-layer PCB.
Within the range of regular multi-layers PCB, we usually call PCB with layers more than 12 as high layer PCB, and call layers more than 16 and drill dia. over 0.3mm and aspect ratio >=8 as backplane.
Build-up multi-layer PCB are also called micro-via multi-layer. The most typical type of build-up multi-layer PCB is HDI with full name high density interconnection. The HDI board often has below parameters: minimum line width/line space below 0.075/0.075mm, minimum diameter <=0.15mm and with buried and blind hole.
HDI are classified to 1+N+1, 2+N+2 and high level. Currently most of the HDI boards are 3+N+3 and 4+N+4, for those above 4 are Any Layer, which are often called ELIC(every layer interconnect). We can often see Any Layer with 10, 12 layers at electronics.
by toughness it can be classified to rigid printed circuit, flexible printed circuit and rigid-flex printed circuit. Note the rigid-flex part are designed as integrated parts not just combined together.
by assembly type it can be classified to through hole mounting PCB, surface mounting PCB and IC Substrate (IC Carrier). Normally substrate has two types: one is unit base FCBGA(Flip Chip Ball Grid Array) and Strip base BGA(Ball Grid Array).
FCBGA does not has many types, frequently we see 4~16 layers, which is the most difficult in PCB manufacturing industry. For BGA there are many types, such as BOC(Board on Chip), PBGA(Plastic Ball Grid Array), CSP(Chip scale Packaging), SiP(System in package), FCCSP(Flip Chip Ball Grid Array), layers from 1 to 10.
by wire forming method it can be Subtractive/Tenting, MSAP/MASP+(Modified Semi-Additive Process), SAP(Semi-Additive Process), etc.
PCB can also be divided as cored or coreless. For coreless there are regulay coreless, ETS(Embedded Trace Subtrate), EPP(Embedded Pattern Process). By surface finishing it can be classified immersion Tin, plate gold(hard gold, soft gold), plate silver, OSP, SOP(solder on Pad).
Above are divided by technical means, but actually we often see classification in mixed method, such as: single layer PCB, double-sided PCB, multi-layer PCB, HDI PCB , IC embedded, rigid board, rigid-flex board, etc.
These are mainly effected by market trends.