There is a difference between Shivaratri and Mahashivaratri. There are in fact 12 Shivaratris, one of which is designated Maha for a specific reason. Moon becomes invisible on amavasya. A day before that, the moon is a very thin crescent. This day is dedicated to Shiva as Shivaratri. It is this moon that adorns Shiva’s head.
Mahashivaratri is the last but one Shivaratri of the luni-solar or Vikrami year. It is part of the celebrations marking the coming of the year to an end. Sixteen days after Mahashivaratri comes the full moon. This purnima, the last one of the Vikrami year, is celebrated as Holi. A fortnight later comes amavasya which marks the beginning of Chaitra the first month of the new Vikrami year. The first nine days are marked as navaratris, with the last of the nine celebrated as Ramanavami. There is an element of over-simplification here. Because Hindu festivals are calculated on the basis of tithi and then transferred to a civil day.
In principle, the beginning of the lunar month of Chaitra is related to spring equinox. The Christian festival of Easter is also related to the spring equinox. That is why. Good Friday/Easter are Ramanavami occur close to each other.
Let us take a look at the list of Indian national holidays and check that Mahashivaratri, Holi, and beginning of spring Navaratri indeed occur in this sequence, a fortnight apart. ( In the Table below, Ramanamai is listed rather than the first of Chaitra.)