No buffer pool and VAS are not the same thing. In SQL Server direct physical memory access is not allowed any memory request which comes is first mapped to process VAS and then if SQL Server find memory free it would map this VAS address to physical memory and then memory becomes committed.
Bufferpool is physical memory VAS is virtual memory.
VAS is Total amount of Virtual address space visible to process. Total VAS in windows OS is divided into VAS for OS process and VAS for application. SQL Server runs as an application. For 64 bit system total VAS is 16TB. So now both SQL sever and Windows process gets VAS of 8TB.
Whenever a new process wants to read data or write data into memory it would reference memory in its VAS region so the new process would see VAS of 8TB and then it would be mapped to physical memory. This physical meory would be your buffer pool
A buffer is an 8 KB page in memory, the same size as a data or index page you can consider buffer as a frame which holds data and index pages when they are brought from disk to memory. SQL Server buffer manager manages the task of reading data pages into buffer pool and also writing it to disk. It is a reserved memory store for SQL Server and by default if you do not set value for it it will take as much memory as possible. Buffer pool only allocates memory to requests which requires less than 8 KB pages this feature changed in SQl Server 2012 where buffer pool has no meaning its just consumer. It is easy to allocate small contiguous amount of memory than large contiguous amount( Large contiguous amount might not be free or present to allocate).
32 Bit system
In 32 bit system SQL Server has VAS of 2G. If system is WOW it would have VAS of 4 G. So this becomes limitation for process which requires huge amount of continuous memory and such memory is not satisfied from buffer pool but outside buffer pool.
"..MultiPage allocation happens in the VAS Area and Single page allocation comes from Buffer Pool..."
This statement is only true for SQL Server 2005 to 2008 R2. Page allocation >8KB is not done by buffer pool. The allocator which does page allocation for buffer pool is
single page allocator while allocator which does allocation for memory pages >8KB is
multi page allocator and memory to this is allocated outside of buffer pool.
For SQL Server 2012 there is
Any page allocator which does allocation for both pages <=8KB and pages >=8KB