No. Bitcoin Core is software that participates in the chain’s network. They are responsible for maintaining the chain, broadcasting transactions along other roles. Everyone and anyone can run one and is encouraged to do so. 

“Owning” bitcoin means that you have the keys over some amount of bitcoin.  This might be on lightning or the main chain itself. You don’t have to run a node to use bitcoin, and the nodes cannot take your bitcoin. They only maintain the list of whose bitcoin belongs to who, effectively.