What really matters, is not the name of the ticket (unless you work for Passenger Focus and are easily fooled

) but the
conditions. Passenger Farce, err, Focus, insisted that the names were "simplified", however the names are in many ways
more complex (such as Off Peak Singles which cannot be bought singly), Passenger Focus did nothing to get the TOCs to simplify the names of the tickets. Until this toothless organisation is replaced or overhauled, and/or the DfT stop being anti-rail, things will continue to get more complex.
You have the old Saver tickets now called Off Peak but they have traditionally been valid on any scheduled train for non-London area journeys and on the ECML that is still the case, and on the same route you can have a ticket that ATOC claim is the same "type" (they only admit to there being "three types" - Anytime, Off Peak and Advance), yet it is valid after something like 9:30am just because it is suffixed with the word "Day". How on earth does that make sense? Two tickets of the same claimed "type" both claiming to be off peak, but one is valid at peak time and the other isn't?
The "Off Peak" is usually less restrictive than the "Off Peak Day", but sometimes the reverse is the case. Again, ATOC don't admit that these are seperate "types" of ticket! Some Off Peak Day tickets count the evening peak as peak time, and bar the use of these tickets at certain times in the evening but generally most tickets do not restrict in the evening. One company that recently implemented this claimed that it is to be "in line" with other train companies, despite no other companies on their route doing this!
The conditions are set by the TOC that sets the fare, and on a route such as the ECML you have a situation where slight variations in origin/destination mean a different TOC sets the fare, so completely different restrictions apply. e.g. Darlo-Wakefield is NXEC, so to travel at 8am will cost you £36.90 for a SVR, but Darlo-Leeds is TPE so to arrive in Leeds before 0930 will cost you £40.10 (yes, more than to Wakefield on the same train!) but even cheaper is Darlo to South Milford which is valid via Leeds at only £24.70 and valid on any scheduled train. Darlo to Sheffield and Dronfield are both £39.90 at any time as NXEC set the fare, but go less than 5 and a half miles beyond Dronfield to Chesterfield and CrossCountry will try to defraud you by charging you a whopping £79.00 as they deem the £43.70 SVR to not be valid until 0930 from Darlo! So that's £35.30 that CrossCountry are defrauding customers on that route, yet you could simply get a Dronfield ticket and on board the Northern train hand £1.70 each way or £2.90 to the conductor to extend your journey to Chesterfield.
Actually, looking back at Darlo to Wakefield it is even more complicated. Route Leeds SVR is £33.40 but not valid for trains that arrive in
Leeds before 0930, the SOR at £41.00 is pointless (other than being able to buy on board) because the SVR via Any Permitted route is only £36.90 and is valid after 0400 which means it is valid on any scheduled train.
Some TOCs (notably Cross Country) are defrauding customers of what must be £millions each year by charging them rates that are considerably higher than the correct fares. By 'correct' fares I mean what the fares should be given the prices charged by reasonable TOCs for the customer occupying the exact same seat on the exact same trains but by asking for a slightly different ticket. It is fraud because Cross Country disguise these products (e.g. "Off Peak") with the same name as a reasonable product priced by NXEC. This product is, however, not the same product at all, despite the name being the same, it is far, far more restrictive and useless for many customers. This forces customers to pay considerably more money than they should have to. The conditions were secretly changed by CrossCountry without the consent of the other party (the customers) and are not advertised except on secret documents ("The manual"/FRPP) or through means which the general public does not easily have access to (Avantix Traveller is not advertised and costs money), also they bar their staff from giving advice to customers on how to avoid the fraudulent "off peak" tickets that are falsely passing themselves off as a ticket that is equal to the tickets with the same name set by other TOCs for the same journey.
So every time you travel you have to undertake research to ensure you are not being unfairly charged by a TOC, and you have to determine whether it is cheaper to buy a ticket to go further or to split the ticket in order to avoid being ripped-off.
Before privisation all these "off peak" tickets (Savers) were valid at any time unless they were for travel into London (and places just outside e.g. Stevenage, Reading etc), so non-London Savers were always unrestricted. They all had the same terms. Now you get companies passing off inferior products as the same great product that we used to have throughout the country, and there is no way to tell by looking at the ticket which is the genuine unrestricted article and which has had unfair restrictions imposed on it by stealth by the likes of CrossCountry and other like-minded anti-customer companies.