When you start a 1v1 game and get thrown into a Terran vs Terran matchup, there's a lot of different strategies that you can begin with, so you better decide quick! I'm going to give you an overview of the basic Terran vs Terran strategies that you can use to win more of these mirror matches and have more fun doing it.
Let's get started…
Early Game
Since this is a mirror match, you're going to have to play better and more cunning than your opponent to win. Whatever you do, he can do, so it's a little different than the other two matchups.
When you first start out, you can choose to harass your opponent if that's your play style. There are a few rush builds that you can use to weaken his economy or take him out entirely if you're lucky.
Banshee rushes are very effective, especially if you get cloak early on. Just by getting a couple Banshees with cloak and separating them, you can get your opponent to blow a couple scans, which can really help you pull ahead in the economic battle.
The Thor rush is a strategy that I personally love doing and is pretty hard to defend against. Thors are so powerful, especially with SCV backup, they can take out Tanks and Marines with impunity. A big group of Marauders may give your Thor trouble, but that's about it.
A Reaper rush is another strat that works pretty good against Terran. If you get your Reaper over their early enough you'll be able to take out SCV's and his Marines that he is defending with. Marine/Marauder rushing can be viable if you're quick enough. Many times your opponent with have a Bunker down too soon to be able to bust it, so use this at your discretion.
In the early game keep in mind that you may have all these rushes coming against you as well, so scout often and prepare accordingly. It's a good idea to build all your buildings right around your base, so you won't have as big a problem with early Banshees and Reapers. Build a bunker right next to your Command Center so you can fight off any early attacks.
Mid to Late Game
When you're playing a Terran player, there is usually a lot of Siege Tanks involved. If you can take the middle of the map with Tanks, it will be very hard for him to break your position. One of the best ways to secure the middle is to build some Missile Turrets out there to keep any Banshees or Medivac drops away.
If you're on the other end of this, don't go for a frontal confrontation. Try to get air control, and sneak some Medivacs into your opponents base to take out his economy and key structures.
Always try to figure out where the weakness in his army is. If your opponent has a ton of Tanks, his army will be very slow, so use mobility to outmatch him and keep him guessing where you're coming from.
Having air control can be really helpful as it can allow you to use Medivacs. Drop your own Tanks onto high ground near his base, or drop Marines into his mineral line. Plus if you can get a group of Banshees over his Tanks they'll go down quick.
Many Terran vs Terran games will come down to a pure resource battle. Because there's no big unit counters (since you can each build the same) you're going to have to rely on your economy and micro skills to win the game. After the early game, these games tend to drag out for awhile, so expand early and often to keep up with resources.
Always upgrade your Command Centers to Orbital Commands and use your scans often to keep track of your opponents movement and base locations. Scout around the expansions with your Vikings and/or just plant a Marine at each one to give you an indicator of when your opponent is expanding. Letting him get free expansions will put you behind in resources, especially when they can be taken out so easily (most of the time)