Correct. When explaining it to students, I have used the metaphor of a housing developer building homes in a subdivision: going to the OS to "allocate" virtual memory is like getting a building permit from the government for a large swath of land. Having permission to build is not the same as a house actually being on that land (which is analogous to physical memory).
Much as housing developers are incentivized to get permits for a large block of land at a time, general purpose memory allocators are incentivized to ask the OS for permission to use large blocks of virtual memory at a time. Asking the OS for virtual memory is very slow, so to avoid doing it a lot, general purpose memory allocators ask for big chunks and manage those chunks themselves.
On modern 64 bits architectures, you have plenty of it to spend. To give an idea of how much of it you have: since Linux 2.6.11 on x86_64, one can address up to 128 TiB (that's 128 thousands of GiB) of virtual memory per process. Starting with Linux 4.12, one can address up to 128 PiB (that's 128 millions of GiB) of virtual memory per process. That's completely unrelated with how much physical memory you have.