According to the fares manual, the 7 Day Standard Season from Manchester to Sheffield is £73.30. This is valid on on train, with any operator, at any time. The £110.00 quoted on a previous post is the "7DF", which is 7 days First Class.
There is a TPE only season ticket between Sheffield and Manchester.
It is called an "Earlybird" and has some time restrictions. It is priced at £45.30. The entry from the Fares Manual is this:
Early Bird Season Tickets - First TransPennine Express
Available as either a Weekly or Monthly Ticket.
Available in Standard Class Only.
Outward travel must be on a service that is due to arrive before 07:30.
Return journey must depart between 10:00 and 16:00, or after 18:30.
The Early Bird Plus is available at £6.00 for those customers who need to travel during the peak for the day of purchase. This must be purchased before the customer boards the train.
Essentially, it is only valid on TPE services between Manchester and Sheffield, and in the morning you cannot travel on the 0720, 0820 or 0920 from Man to Shf, coming back you cannot travel on the 1610, 1710 or 1810 from Shf to Man. If you wanted to travel on these train you would need to buy a £6 "Early bird Plus" supplement from the ticket office prior to travelling. This supplement is valid for the day, both directions, so you only need to pay once per day. Again though, this would still only be valid on TPE services so you could not use EMT or NT.
Now obviously if you travelled only 4 days a week, even at peak times, you could buy an EarlyBird season for £45.30, then pay £6 each day (£24) which gives a total of £69.30, thus saving a few ££. If you travelled 5 days a week, but could restrict yourself to the time restrictions detailed above even 1 day a week, then are still saving a few ££. What you save in ££ however, you loose in flexibility.
One other point. These tickets were essentially designed for commuters into Manchester, and some literature will say you "must arrive in Manchester before 0730" for example. These tickets are however accepted the same as point-to-point season, as long as you comply with the time restrictions above depending on which way you are going. So, in theory you could travel form Man to Shf on the 1020 and come back on the 1910.