Warning, Warning

If you use the word, “beware” you are warning someone of something dangerous.

Be Aware

The term “be aware” has the description of having information and beforehand knowledge of a situation, and perception of a fact that may become important in some way.

Be Wary

“Being wary” arises from, or is characterized by, caution.

Conclusion

The words seem related, insofar as there is danger (perhaps) involved, but the degree of warning is the subtle difference.