The total sum of squares = treatment sum

I am confusing Sum of Squares information.  Can you please tell me the difference between these two:
The total sum of squares = treatment sum of squares (SST) + sum of squares of the residual error (SSE)
Versus:
When computing F stat you use
Between group SS/(g − 1)
Within group SS/(g(t − 1))  Isnt Within Group SS then effectively the SSE?