What is the difference between a re-boot and a remake? To step out of gaming for a minute, to me the change between the 80's and 90's Batman movies and to the Christopher Nolan Batman trilogy is a remake. While from Nolan Batman to Superman v Batman, that is a reboot.
So a remake is when restart the franchise or story when there has been sufficient enough time between the last installment of the old series and the beginning of the new series that you would not consider them contemporaries or peers.
On the other hand, a reboot would be a restart where the last installment of the older series and the restart are contemporaries.
Batman & Robin came out in 1997, Batman Begins was out in 2005. Batman & Robin was still using the 80's no one really dies cartooin movies, while Batman Begins was the super gritty realism. Different tone, different feels, different vision. It is really hard to say that B&R and BB are contemporaries. Clearly a remake.
Dark Knight Rise came out 2012. Batman v Superman comes out 2016. Clearly they are restarting the Batman character. But we can tell that it is using a lot of the same tone, same gritty feel. Also with Man of Steel coming out in 2013, with Batman v Superman being the sequal, clearing a series that ended a year before then next one began are contemporary. Reboot.
So then applying these definitions to video games, Master of Orion is a remake. The last in the original MoO series was out in 2003. The new MoO is restarting the series and in 13 year, enough gaming conventions have changed, it would not be fair to call them contemporaries. Therefore you it is a restart not a reboot.
The reason all of this matters is that to me a restart is fairly begnin. It more of has the connotation of breathing new life into an old series. While a reboot tends to be more negative.