Titanfall 2 builds uppon the core design elements of the original.
In short, Titanfall 1 gameplay consisted of combat between pilots with the abilities to double jump and wall run and Titans, 3 story tall Mechs one could call down after several minutes or engaging in enough combat. Various factors, most notably the agility of the pilots and the ability to duck into buildings for cover, compared to the raw power of titans, served to balance combat between the two modes of play. Various NPCs including footsoldiers and terminator-like Spectres also take part in combat, and to a lesser extend the wildlife, however the general effectiveness of the NPCs relegated them to more of fodder for pilots to increase build time and farm some points. Titanfall 2 includes various tweakes and additions to the formula of the original game.

Single Player Campaign
    The biggest addition to the game is a single player campaign which was absent from the original game. The story follows a soldier who becomes a Titan pilot as well as the bond he shares with the titan he is partnered with. Level design is built to lend itself to compliment the movement abilities you have as a pilot as well as abilities as a titan, with movement puzzles and combat scenarios that encourage use of all of your abilites.   Dialouge options exist within the game but will not impact the overall narative.

Pilots
    The standard movement mechanics have been changed as so to encourage use of more of your movement options, as opposed to Titanfall 1 where it was easy to gain max speed by simply spamming bunny-hops.
Even more equipment options are now available for pilots, including  a grappling hook to further increase mobility options.

Pilot Equipment
 
    Use of some equipment has also been tweaked, namely Burn Cards. In titanfall 1 you could carry up to 3 single use burn cards at once. These cards contained various power ups such as, but not limited to amped weapons or permanently active armor abilites, such as cloack or stim. These cards could be activated at the start of the match or after any death at the pilot's dicression. Burn cards have been removed from Titanfall 2 and replaced with Boosts.

    Boosts are now a part of your loadout, as opposed to Burn Cards which were consumables. You may only pick one Boost as opposed to the 3 burn cards. Each boost has an unlimited number of charges, however, they must be earned, rather than activated at will by charging up your titan build meter  to a certain percent based on whichever boost you are using. And with the mention of the titan build meter comes another very important change.



Titans

    Titans in titanfall 1 were built on a timer of 4 minutes for the initial build and 2 minutes for any subsequant rebuilds, and time would be reduced for every shot landed, or kill obtained, or machine hacked. Titanfall 2 no longer has a timer for guaranteed builds. Pilots now MUST, engage in combat to progress the completion of their titan.

    Titans themselves have also undergone massive changes. They seem to no longer include body-sheild generators, however their health can now be regenerated using battery cores taken from other titans by rodeo attack, a mechanic that has also seen its share of changes. After stealing the core of a titan, a rodeoing pilot is ejected from the titan's back and must re-board that titan to begin throwing  grenades into the titan's exposed core.
Doomed state is another titan mechaic that has changed dramatically. Doomed titans no longer have a limited time of survival, and will continue to function until their bar is depleted or they are hit with a melee attack from another titan, which will result in an exection.

    Perhaps the most major change to titans comes the changes to titan Chassis and customization. Customization of Titans has been reduced significantly. The only choices for Titans will be the Chasis, the Skins and a couple of pasive perks. However, Titanfall 2 now sports 6 unique chassis each with their own set of abilities and play styles.