An address is a string derived from a public-key, or assigned to a deployed contract. It is safe to share, and all activity against it is permanently public on a block-explorer.
Addresses are network-specific in practice. The same string may be valid on several chains with identical formats, which is how people lose funds by sending an asset over the wrong network to an exchange that only credits one of them.
Practical rules: always verify the first and last several characters against the source, send a small test amount first when the sum is meaningful, and beware address-poisoning, where an attacker seeds your history with a lookalike address hoping you copy it.
Related: public-key, address-poisoning, block-explorer, ens-name