Handset phone jack converter?

First of all, what are the official terms for the following:

1. Phone cable.
2. Handset jack phone cable (thinner plug than normal phone cable).

And then,

I need to convert a female thin phone jack to a think male normal phone cable.

And I need to do the opposite too- convert a thin (hanset) male cable to fit into a think female. It fits but it's loose and wobbles.

Are there converters for those? Radio shack?