Why can a 32bit operating system only see 4GB RAM but can see 2TB hard drives?

that is because it uses LBA - block adressing :
https://en.wikipedia.org/wiki/Logical_block_addressing

Technically the premise of your question is wrong.   32-bit operating systems can see far more than 4GB, but can only directly address 4GB.    To USE more than 4GB requires some form of address extension, whereby the memory is addressed in pages, which can be mapped in and out of the 4GB address space the CPU can physically address.    Microsoft does this using PAE (physical address extension), which allows a 32-bit CPU to address up to 128GB of memory.

However, they only implemented this on server versions of Windows, and how much can actually be addressed is a function of the specific version of the OS.   For example, Server 2008 can address 64GB with the 32-bit version.

By the way, 32-bit versions of Windows from Vista on can see disks far larger than 2TB, as they all support GPT disks -- so you can use modern 6TB, 8TB, 10TB, and even larger disks.

64GB to be accurate (4 bits in PAT for address selector)
Single 32bit process is limited to 4GB address space, on a 32bit system it uses same address space for system calls, on 64bit system it can use all 4GB for itself.

Microsoft's implementation does indeed restrict the max total to 64GB ... although there was a version fo Server 2003 DataCenter Edition that supported 128GB with 32-bit CPU's.   But they've since restricted their 32-bit servers to a max of 64GB because of the easier implementation.

It is not possible with PAE
https://msdn.microsoft.com/en-us/library/windows/desktop/aa366778%28v=vs.85%29.aspx?f=255&MSPPError=-2147217396#physical_memory_limits_windows_server_2003_sp2
Not possible on Linux either.

From Mark Russinovich's blog on "Pushing the Limits of Windows: Physical Memory" ...

"... The maximum 32-bit limit of 128GB, supported by Windows Server 2003 Datacenter Edition,  comes from the fact that ..."

It accomplishes that through a PFN database that is used by the memory manager to track the pages and map them into a virtual space.   Microsoft did not choose to continue this scheme in subsequent server versions, since they could get better performance with the 4-bit PAT, which limits the addressing to 64GB, but it IS possible to support more.

There is no such OS ever released.
PAE and PSE both go to 64GB ditto.

Regardless... the basic answer to the original question is that RAM is addressed in bytes while disk space is accessed in 512-byte blocks.  There can be a lot more details but that's the basic answer.

There are simple algorithms to do double-width math (or quad)
There should be no problem supporting exabytes on a 32bit system.
There is some practical limits though like how much address space is needed by practical on-disk structures in each case etc.

"... There is no such OS ever released. " ==>  I presume you know who Mark Russinovich is ... founder of WinInternals;  Microsoft Technical Fellow (after they bought his company); and one of the most respected experts in Windows technologies.   The quote above is from his blog here:

https://blogs.technet.microsoft.com/markrussinovich/2008/07/21/pushing-the-limits-of-windows-physical-memory/

Excel still makes blatant rounding errors...
If you read coments you see a lots of sceptics (especially show that 32bit system with 128GB support)

Thanks everyone for helping me to understand.

i was the first to post the solution - and nothing??

Apologies.  I thought I had tagged the top 3... I don't seem to be able to modify my answer.

you can if you want to - by using request attention
but tx anyway