Stuttgart to Tubingen Trains

Can someone explain the difference between two types of train tickets to me for a day trip from Stuttgart to Tubingen ?

Somehow self-explaining by the name: the difference is the reach of validity. Click on links for detailed info in German.
MetropolTagesTicket Stuttgart: the tariff cooperation for the Stuttgart region. From the Swabian Alb to the Danube valley.
Baden-Württemberg-Ticket: 1 day through the whole state. On local trains even as far as Basel.

On weekend days you can start your journeys before 9 a.m..

The Metropol/Tages Ticket is 31 EUR for 2 people, and you can take any train to and from at any time after 9 am weekdays (anytime weekends). Buy when you get there on the day of travel from a ticket machine as there is a 2 EUR surcharge if you buy from a human at a ticket window. Yes it is valid for other journeys the same day within the area of validity, which includes Esslingen and Ludwigsburg.

In Tuebingen I used 3 different daily passes, depending on my travels that day. Just choose the cheapest that meets your day’s journey

Just keep in mind, if you are looking at several days of travel, a Deutschland Ticket at 49 euro for each of you might make sense, covers all the trains/buses/trams the above two passes do, plus no regional or time restrictions. I bought through Tranzer, process was simple and easy, a single transaction using a US Credit Card, they cancel, so easy (they do charge a 2 or 3 euro fee).

So for a day trip from Stuttgart to Tubingen a MetropolTages Ticket for €31.50 would serve our needs well and you say is valid for other journeys the same day within the area of validity, including Esslingen and Ludwigsburg.
Just to confirm, it would also cover local U Bahn travel within the city of Stuttgart, too? Using this ticket we could leave and return from the Bihlplatz stop in Stuttgart near our Airbnb and not need to buy a separate VVS Group Day Ticket?

What is the difference between traveling on IRE, MEX , RB and SB trains. The prices are the same and I see some time duration differences. Anything else?
Also, the MetropolTages Ticket can be purchased as a mobile ticket on the DB app, correct?

The Metropol/Tages Ticket is 31 EUR for 2 adults, not 31.50 EUR.

S, RB, RE, IRE, MEX trains are all valid for the Metropol/Tages Ticket. These are just various forms of regional trains. The ones with shorter travel times have fewer stops along the way, thus they are faster.

Yes, it is valid on U-Bahns and local buses. I would assume it would work on the DB App. Just remember that it is nonrefundable, so buy day of travel when you are sure of your travel needs.

What is the difference between traveling on IRE, MEX , RB and SB trains

Functionally, all are the same, you can't even really say there is quality difference, since equipment for each can vary from old cars to brand new ones. About the only difference may be in travel time, the RB and SB trains likely are slower, due to many stops. Anything with an E or EX in the description typically means express, which denotes fewer stops. However, just take the one that best fits your schedule, looking at arrival time at your destination. Typically the first train that comes along is fine, in a rare instance, you might be able to wait 10 minutes, but catch a train that gets your there 10 minutes earlier.