Help me understand the Rails. What happens if you miss the train or want to take an earlier train?

The app and the website are the same. An advance ticket locks you into one particular train so make sure you’re on it.

In general, if you buy an advance ticket and miss your train or want to stay longer, then you will need to buy a new ticket. If you want flexibility, then buy a less restrictive ticket at a higher price.

The man in seat61 has a brief summary of the various fare types.
https://www.seat61.com/UK-train-travel.htm#30%20second%20guide%20to%20UK%20rail%20fares

Advance tickets - with a capital A - are for one precise train at one and only one time. Other than the exact train named on the ticket they are worthless, but good to use as a bookmark.

If you wish to change the time they can be exchanged in a booking office prior to the departure time on the ticket. That is very expensive though - most train companies charge a £10 per ticket change fee and then charge you the difference between what you paid and the walk-up fare available at the time for the train you wish to board. In other words, more expensive than buying the walk-up ticket at the time.

This change must be made in the booking office and cannot be made on the train. On the train you are liable to be treated as having no ticket and being required to pay a full fare ticket - even more expensive. If you are caught without a valid ticket by a Penalty Fare Inspector you are also liable for a fine.

What circumstances are you envisioning? Can you clarify your situation a little please?

Anytime tickets and Off-Peak tickets are valid on any train (with operator and route restrictions) in the class in which they are issued during their validity period so you can change at will within those restrictions.

One way around the very high fares for longer distance travel yet still not have to pre-book specific train(s), is to split the ticket into sections - points at which the through train stops. This site tells you how:>https://new.trainsplit.com

Fares for shorter journeys usually do not mean that you have to be on a specific train. The cheap ‘Advance’ fares apply to long distance specific trains and the fares get loaded to the system around 11 weeks ahead - usually.

Fares tend to be highest at commuting times and in Fridays due to high demand. Some return fares are only a £1 or so higher than one way fares. See www.nationalrail.co.uk

I know this is more expensive than advance tickets, but I prefer to just wait until after 9:30 AM and take the train that suits me.

Yes, it is at 9.30am on weekdays when lower fares kick in. They also apply all day on the weekends though Sundays in particular can be prone to engineering work. If you must buy an advance ticket that leaves before 9.30am - you will usually be charged a high fare for the WHOLE journey. If you can find the place that the train reaches just after 9.30am and then check the split ticket price from that station onwards, it can often result in savings.

And referring you back to your earlier post, two ways around the restrictions of Advance fares for your family of 4 include 1) getting ticket discounts on short notice with a Family and Friends Card or 2) buying a multi-day BritRail pass for a pre-set price that can be used to hop on any train.