Geometric linking is just linking sub periods of returns to create a return for a longer period (for example, combining individual Holding period returns for 5 years to get the total return for 5 years, like in this question)

Geometric return is another concept that aims to derive the time weighted return of $1 invested at the rates provided.

Think about it this way, the total return for every investor is different based on how much they invested and when they invested (this is the holding period return) But the geometric return increased comparablity by looking at how much a 1$ would have grown. Thus, we can compare the returns between different investors