Current source vs current limiter
Yes, you're right, but the figures you posted are the same configuration: they regulate the current over the output resistor measuring its voltage drop.

The basic difference between a voltage source and a current source, is that the first has a low output resistance (ideally 0), while the current source has a high output resistance (ideally infinite).

The voltage source with current limiting is made to provide a constant voltage in its operating range, but drops the output voltage as protection mechanism to prevent damaging the load and the source itself. Note that there are different methods of current limiting, one of which brings the current below the limit to prevent overheating.

In practice you can use a current limiting source to generate a specific current, but while a supply can handle it without problems, for an integrated devices is not a standard operating mode, and can result in wrong behavior.