I have seen shameful and shameless being used interchangeably, but it is surprising that they would mean the same.
Is there a difference?
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"Shameless" means pretty much what you'd expect: that someone should feel shame at something, but doesn't.
"Shameful" can have two meanings that almost seem like antonyms, but they're not, depending on whether it's applied to a person or an act. If it's applied to a person, it generally means that they feel remorse. If it's applied to an act, it means that whoever is performing the action should feel shame. However, it's often used to emphasize that the person should feel shame, but doesn't. In this latter sense, it can almost seem like "shameful" means the same thing as "shameless".
The existing answer is largely valid, but just to add my British English perspective...
The words can often have similar meanings, but the contexts in which they are used are almost always slightly different. A crucial difference to note is that "shameless" implies that someone does not feel any shame (for an action), whereas "shameful" does not at all imply this; the person may or may not recognise the shame of their action.