If you send a pcb design to be manufactured (to a "UL-approved" fabricator) with no materials specified at all, you should still receive an acceptable board for most applications. In other words, even without drawings or notes or instructions, and in the absence of any specific requirements, the fabricator still has the responsibility for using materials that provide proper interconnection between components and that provide adequate insulation between PCB interconnecton points that should not be connected, or you shouldn't have to pay for the boards.
If you know in advance which fabricator will be manufacturing your boards and you have the ability to communicate with them, take the initiative to find out which materials they prefer to use. Don't be afraid to share your design criteria with them and discuss whether their default materials are adequate for your needs, or if you should PCB specify something more robust. Regardless, don't hesitate to specify at least the general "slash sheet" number of material that will be adequate for your design needs.
Here is an example of a simple note to specify board material:
All material must meet or exceed the requirements of ipc-4101/24 at the other extreme, here is one recommendation for a note specifying materials used in a rohs-compatible high-reliability product:
Base material shall be flame-retardant rated ul 94v-0 laminate glass fiber epoxy and pcb conform pcb to type l126 (gfg) according to ipc-4101/126.
Base material requirements: a minimum glass transition temperature of 170℃, as tested according to ipc-tm-650, 2.4.24c; A minimum decomposition temperature, td(5%) of 340℃, pcb as tested according to ipc-tm-650, 2.4.24.6; A t-288 delamination time of 10 minutes minimum, as tested according to ipc-tm-650, 2.4.24.1c; Maximum thick-ness-direction thermal expansion of 3.0% from 50 to 260℃.
Prepreg material shall conform to type p126 (pgfg) according to ipc-4101/126 and be subject to the same requirements as pcb the base material.
There may also be reasons for specifying laminate thicknesses to control the distance between individual layers. Examples could be:
specifying a minimum distance between layers to maintain a voltage clearance requirement;
specifying a maximum PCB separation between power and ground planes to maintain capacitance for decoupling;
specifying a desired distance between layers to achieve impedance targets.
For reasons such as these, you should also provide a desired layer stack-up with any requirements noted, and make sure to include the overall finished board thickness.
Keep in mind that this is only the briefest overview possible to introduce the concept of PCB board materials. I have to focus on the most common type of board construction, but you should understand that there PCB many options available for a wide variety of applications including flexible circuitry, metal-core constructions for high-temperature, exotic materials for high-speed signal propagation, special materials for High-Density Interconnect (HDI), materials for buried capacitance, etc. Each of these materials will have its own set of unique properties that contribute PCB to the desired performance.