Bricks are extremely variable in composition, density and ability to withstand temperature.
Basically, in most cases bricks have a fairly simple task to do and are made from the cheapest material that will get the job done. Because transporting bricks is expensive, cheap generally means local and the composition of bricks is dependent on the local geology.
As the job the brick is used for gets more demanding, the specification gets tighter and the bricks usually need to travel further (on average) and get more expensive.
Bricks used in hot, arid regions can be quite porous, for example, whereas those used in damp climates with cold winters need to be waterproof to prevent them absorbing water and cracking as it freezes; a tighter spec..
The strength requirements when constructing two-storey buildings are relatively low. For twenty storey buildings the bricks need to be considerably stronger.
I live just down the road from Accrington, England, where the extremely hard bricks used in the foundations of the Empire State Building were made. The cost per brick on that job was obviously pretty high and included 3000-plus miles of transport. However, all the houses round here are made from the same brick because it's local and therefore cheap.
Where the job requirement is for a brick able to withstand high temperature, the number of places with the geology to produce such bricks is relatively small.
There are some places that have local deposits of fireclay and their local brick is therefore effectively a firebrick (or passably close to one). Over here, these bricks are often buff-colored.
The local Accrington Nori bricks are red, but are also made from a fireclay and are able to withstand high temperatures. In combination with their extreme hardness, this made them ideal for building the very tall chimneys that provided the draft for the boilers towards the end of the age of steam.
If you live somewhere that has locally-made bricks from fireclay, you may well be able to use found brick as refractory brick. It could be worth checking around.
Most importantly, if you see that someone somewhere has used found bricks to build a forge, furnace, etc, with no issues, do not assume that a brick is just a brick and that you can safely do the same where you are.
If you are looking to use a solid fuel (charcoal) forge to get started, a hole in the ground and something to produce a draft has worked pretty effectively for several millennia. It might be worth checking out youtube: there's a guy in Devon I know by the name of Dave Budd. He does a bit of Iron-Age metalworking and I've seen him on youtube, so he might make a good starting point.
Almost any decent-sized lump of steel will do as an anvil to start with; cold mild steel is still harder than hot carbon steel. Avoid cast iron though.