The exception is the political capitol. Due to how the bonuses it gives are calculated, it can use the bonus from either a morale or influence bonus tile.
The difference is in how the different planetary outputs are calculated. Manufacturing and research are produced as concrete point values, and the capitol structures increase that output by a percentage. Since the two structures perform slightly different functions, the game recognizes one as getting the bonus and the other as not getting it. A structure that gives a +% to food production has the same issue, and the bonus will not apply to that building for the same reason.
Influence and morale are different, as no structures produce concrete values of either influence or morale. ALL structures for those two categories increase the planet's stats by a % value, so all structures that increase those stats by a % can use the bonus.
Note the above does NOT apply to things like trade goods or galactic achievements. Only structures with effects limited to the planet they are built on can receive tile bonuses. Anything that affects your empire as a whole cannot use a bonus tile.