What is the difference between encrypting and signing in asymmetric encryption? [closed]

What is the difference between encrypting some data vs signing some data (using RSA)?

Does it simply reverse the role of the public-private keys?

For example, I want to use my private key to generate messages so only I can possibly be the sender. I want my public key to be used to read the messages and I do not care who reads them. I want to be able to encrypt certain information and use it as a product-key for my software. I only care that I am the only one who can generate these. I would like to include my public key in my software to decrypt/read the signature of the key. I do not care who can read the data in the key, I only care that I am the only verifiable one who can generate them.

Is signing useful in this scenario?

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