The latter is basically fine-tuning the model with direction from another model. Thousands of businesses do this every day to fine-tune. This is almost certainly what the Chinese labs are doing, since it has a much better effect on the end result than just getting simple answers to simple questions.
These complaints of distillation are inflating the problem to make it sound worse than it is, because they want the USG to block/ban Chinese model providers as protectionism. They have already called for more export controls on chips (which is funny because DeepSeek v4 was designed to run on Huawei chips and now the other Chinese providers are following suit). But they can't come right out and say that, so their claim is that they're asking for more export controls because distilled models might not be as safe as their own. But if you show them a jailbreak of their model that bypasses their safety, they'll tell you that any model can eventually be jailbroken so don't worry about safety.