Atoc says passengers wanted a simpler system of tickets
The second phase of a simpler rail ticketing system has come into operation, with just two categories for buying tickets on the day of travel.
The new fares are "anytime" - which can be used on any train, at any time; and "off-peak" which has restrictions on the time and day of travel.
The move comes after a revamp of the advanced tickets structure in May.
Watchdog Passenger Focus has welcomed the new fares, but others say greater changes are needed to the rail network.
"Adopting common ticket names is a step in the right direction," Anthony Smith, chief executive of Passenger Focus, told BBC Radio Five Live.
"It does start to hack away at some of the complexity of the fares and the names and for the first time we've got all the train companies using the same names".
Current ticket types which will be re-named off-peak include Saver and Cheap Day returns.
Train operators say they are responding to passenger demand and the new changes will continue to make the system simpler.
Michael Roberts, chief executive of the Association of Train Operating Companies (Atoc), told the BBC News Channel said the new structure meant "a variety of tickets to suit all pockets".
Pressure group Campaign for Better Transport welcomed the changes but said train fares still need to be reduced.
Speaking to the BBC News channel Simon Calder, travel editor of the Independent newspaper, said: "We have a very complicated system of tickets in the UK - what they have done is change the labels to try and end the confusion."
He said the proliferation of different ticket prices for the same rail journey was about "trying to squeeze more of us onto an inadequate rail system".
"The label changes happening today may make life much easier for passengers but if you want to travel long-distance you are going to have to book a long time in advance and travel on a quiet train."
In May a new advanced ticket replaced discounted offers such as Leisure Advance, Business Advance, Value Advance and Apex.
The number of UK rail journeys has risen more than 40% in the past decade.