Translation:I have many old chains and wedding rings.
"Old chains and wedding rings" can mean "old chains and old wedding rings" or "wedding rings and old chains". I think that in Romanian is just the same. By the way, the roots of both words are origin of usual Slavic words for "chain". Corresponding to lanț (whence lănțișor), there is Russian ланцу́г (lancúg) or Polish łańcuch. For verigă (whence verighetă) we got Bulgarian вери́га (veríga) or Serbo-Croatian верига (veriga).
OK so summoning up the most miniscule initiative I looked for images of lantisor.
In BrE they are necklaces. They might occasionally be described as chain necklaces, but so far as I know they're not usually described as chains.
Some blokes wear chains around their necks, typically Leisure Suit Larry types, thugs and people trying to imitate thugs.
Still, in this context, in BrE, the word is necklace. Is that different in American English?