Hold sb close/ tight =with your arms around someone.
First of all, both hold sb close/tight can be used interchangeably without changing its meaning. As for its translation, it would be ''abraçar alguem fortemente or simply abraçar as you said. ''. here's an example to clarify a little bit:
Ex: She kissed him and held him tight.
Ex: Ela o beijou e abraçou o fortemente o simplesmente o abraçou.