Both are exemptions under Regulation D and let you raise unlimited capital from accredited investors without registering the offering with the SEC. The difference is in how you find investors.
Rule 506(b): No general solicitation. You can only offer the securities to people you have a pre-existing substantive relationship with. You can include up to 35 sophisticated non-accredited investors, but the disclosure requirements get heavier when you do.
Rule 506(c): General solicitation is allowed. You can advertise the offering publicly, post it online, and pitch it to people you don't know. The trade-off is that every investor must be accredited and you must take reasonable steps to verify their accreditation status. Self-certification is not enough.
The choice depends on whether you have an existing investor network (lean 506(b)) or want to market the deal publicly (lean 506(c)).