The two fall on the same night, and the shorthand is common in non-Sikh writing. Sikhs generally object to it, and the objection is not about pedantry.
The events are unrelated. Diwali gathers several narratives, chiefly Rama's return to Ayodhya, and it is worshipped into with lamps for Lakshmi. Bandi Chhor Divas marks a release from a Mughal prison in 1619 and a Guru who refused to leave without the men imprisoned alongside him. The lamps at Amritsar are lit for that.
The coincidence of date is genuine and old. Amritsar was already drawing large seasonal gatherings at this point in the year in Guru Amar Das's time, decades before the imprisonment, and Guru Hargobind's return to the city was received into a season that already had crowds in it. So the overlap is not modern invention. What is modern is the insistence on the separate name, which spread through the twentieth century and is now standard in gurdwara usage worldwide.
That insistence belongs to a larger and unfinished argument about whether Sikh practice is distinguishable from Hindu practice or a variant within it, an argument conducted through the Singh Sabha reform movement, through the legal definition of Sikh identity in Indian law, and through the calendar. Naming this day is one of the places the argument is carried on. Describing it as Sikh Diwali takes a side in that argument while appearing not to.