I was wondering how bitcoin public and private keys are generated. E.g., a certain number of characters etc. And how one could tell a litecoin address from a bitcoin address for instance.
the private key is only a (very big) integer-number. this number used as private key is all you need to generate a public key with some more or less complex mathematical operations and this private key is also the only thing which must be your secret. anyone can know your address and your public key, no problem. with the public key you can generate the address of the public key. (=>public key and address are not the same.)
a common used format to store a private key is the WIF-format. you can convert a private key to the wif-format and vice versa.
many people call a keypair (containing private- and public key) a "wallet". but technically you don't need any software to have a wallet. you can have a paper wallet for example as long as you do not want so send your funds to have full access to your funds.