Here, in México, we never use a ring inside the top. In my very personal opinion, is not necesary to use at all.
But is possible that in some special and expensives tops, you must be use them, I don´t know.
I think that the second ring you are saying, is the one that is used to put it in the "top of the top" and that is useful to throw it.
In the other hand, the most of USA players, they don´t are very used to play with this ring. And here, is the opossite thing, all the people uses the ring to throw the top. Only a very few quantity of persons take the ring away and do the knot in the capa of the top, without using a ring.
Personally, I never use rings of plastic inside the tops. Only in the trompo Grandes. But it´s the same to me to play with or without the ring inside. I ´ve got a Duncan Ripcord, and I think that the black ring to ber used inside is completly unnecesary.
And, to me is almost completly necesary to play with the ring to throw the top. Besides, doing many tricks, is necesary ..like a counterweight...and you can do at least, a couple of nice trics by using this ring.
Je ne sais pas si cette information será d´aide pour toi.
