The most important thing to remember is -- what matters is not the date on which you begin your travel. What is counted is the date on which the train begins its travel.
Even the railway website is not clear on this important point, though regular travellers, especially who board a long-distance train midway, might be aware of this.
Probably because it depends on the date on which the chart is prepared, at the station where the train originates.
Anyway, I discovered this by chance, when I saw that I could book for one train but not for another on the same day. Thought, I must share this, for people who might not be aware.
Here is an example.
The farthest date for which you can book today (March 19), is May 18. (Currently it's 60 days in advance, but from April 1, it will be 120 days in advance.)
Assume you are booking a ticket from Bhopal to Thiruvananthapuram for May 20.
There are two trains available on that day -- Himsagar Express and Kerala Express. But you will find that you are able to book a ticket in Himsagar Express for May 20, but you can't for Kerala Express for the same date. (The booking should be possible only for up to May 18, and at first look it might look strange why it's possible to book for May 20.)
My guess is (there is no one to confirm officially), this is because, Himsagar Express begins its journey from Jammu on May 18, and reaches Bhopal on the Day 3, that is May 20.
On the other hand, Kerala Express begins journey from Delhi and reaches Bhopal on the same day.
So, you can book in Himsagar Express for May 20, but the farthest date for which you can book for Kerala Express is May 18.
So, so if you are looking to be at the virtual ticketing counter right on the day the Advance Booking Period commences, (now 60 days in advance, from April 1 it will be 120 days), check if you are boarding the train on the same day as it leaves originating station or on Day 2 or 3.