No, the Roman and Egyptian calendars were not the same.
The Ancient Egyptian calendar was a solar-based system of exactly 365 days, consisting of 12 months of 30 days plus 5 extra days. Because it lacked a leap year, it slowly drifted out of sync with the seasons, completing a full cycle through the year every 1,460 years.
The pre-Julian Roman calendar was originally a lunar-based system of about 355 days. It was highly inaccurate and relied on the manual insertion of extra months by politicians to try to keep it aligned with the seasons, which often led to significant confusion and misuse.
The two systems became linked when Julius Caesar reformed the Roman calendar in 46 BCE. After consulting with the astronomer Sosigenes of Alexandria, Caesar adopted the Egyptian 365-day structure for Rome but added the critical innovation of the leap year. This leap year mechanism is what eventually allowed the Roman (and later Gregorian) calendar to stay permanently aligned with the solar year.
It was not until 25 BCE that the Roman Emperor Augustus reformed the Egyptian calendar itself to include a leap day, finally bringing it into line with the Julian system. In short, the Egyptian calendar provided the 365-day framework, while the Roman system provided the leap-year logic that defines our modern calendar today.