Both of these words have the same meaning, but they must be phrased with some implication there. In OED2, the simple difference appears to be that connotation applies to the definition of a single word, while subtext is the meaning in a broader text.

Connotation

1. In addition, inclusion of something in the meaning of the word besides what it primarily denotes; implication. 2 The signifying in addition; inclusion in addition to a verb.
What is b.1? Is added to the literal meaning of an element a word in addition to its essential meaning.

And in logic,

b.2.A. and in logic, b.2. with the logical function of z.S. c As with J. S. Mill and later logicians: An attribute or aggregate of attributes connoted by a term.

What

are few examples? 2 In literature, an underlying theme is discussed (e.g. writing), but should be addressed as a topic. What is an historical novel or a play?

What is the meaning of words “Although English is the official language of this country”, and why was it that English is the language of this country?”