Just like in spoken language, some babies who use sign will use the same sign to mean various related things. For example a baby taught to sign CAT might use the sign when they see a dog for the first time. Rather than being upset, this is cause for celebration. Your baby is doing something rather amazing. He is referring to a four-legged-animal within the same category as a cat. He is using what he knows to generalize from one situation to another.
This scenario can play out many different ways. A baby might call water MILK or might use MORE to get access to many different things. Often a baby will use the sign MORE to want to go outside, or to be picked up. The same thing will happen when baby begins to speak. Since their vocabulary is so limited, a baby will get by on whatever words they have.
When generalization happens, remain positive and encouraging. Acknowledge the word they are using, but don’t be afraid to offer the correct word as a substitute. You might say “Oh, you think that’s a CAT, but it’s not a CAT at all, that’s a DOG.” You then might find other examples of dogs and cats in books if you have access to any or in real life as opportunities present themselves.