What is another word for reffering to the month?

There isn't a single perfect synonym for "month" that captures all its nuances. However, depending on the context, you could use:

Formal:

* Period: "The project is due in the next period."

* Calendar month: "We'll meet again in the next calendar month."

* Lunar month: "The lunar month is about 29.5 days long."

* Solar month: "The solar month is about 30 days long."

* Lunation: "The lunation cycle is a natural phenomenon."

Informal:

* Time: "See you in a time."

* Stretch: "This is a long stretch of work."

* While: "I'll be gone for a while."

More specific:

* Season: "This project will take several seasons to complete."

* Quarter: "The company had its best quarter in years."

* Cycle: "The menstrual cycle is a natural process."

The best word to use depends on the specific meaning you want to convey.