In the following questions "a general offer of evidence" is one in which the offeror does not explain the relevance or purpose of the evidence and "a specific offer" is one in which the nature of the proffered evidence is made apparent to the trial court and the offeror does give a specific explanation (whether accurate or inaccurate) of the relevance and purpose of the evidence.

1.

PP makes a general offer of evidence.
DD makes a general objection.
The trial court sustains the objection.
Verdict and judgment are for DD.
PP appeals.

Who wins?

Does it matter whether PP's evidence was admissible?

2.

PP makes a general offer of evidence.
DD makes a general objection.
The trial court overrules the objection.
Verdict and judgment are for PP.
DD appeals.

Who wins?

Does it matter whether PP's evidence was admissible?

3.

PP makes a specific offer of evidence.
But PP's explanation of the relevance and purpose of the evidence is incorrect.
DD makes a general objection.
The trial court sustains the objection.
V & J are for DD.
PP appeals.

Who wins?

Does it matter whether PP's evidence was admissible?

4.

PP makes a specific offer of evidence.
But PP's explanation of the relevance and purpose of the evidence is incorrect.
DD makes a general objection.
The trial court overrules the objection.
V & J for PP.
DD appeals.

Who wins?

Does it matter whether PP's evidence was admissible?

Cf. Problems 6 & 7, below.

5.

PP makes a general offer of evidence.
DD makes a specific objection.
But DD's specific objection is incorrect.
The trial court overrules DD's objection.
V & J for PP.
DD appeals.

Who wins?

Does it matter whether PP's evidence was admissible?

6.

PP makes a general offer of evidence.
DD makes a specific objection.
But DD's specific objection is incorrect.
The trial court sustains DD's objection.
V & J for DD.

PP appeals.
Who wins?

Does it matter whether PP's evidence was admissible?

7.

PP makes a specific offer of evidence.
But PP's explanation of why the evidence is admissible is incorrect.
DD makes a correct specific objection to this explanation. But the trial court overrules DD's objection -- because the evidence is admissible for a reason and purpose not stated by PP.
V & J for PP.
DD appeals.

Who wins?

I can only guess at the answer to this question. What's your guess and why? Cf. Problems 4 and 6, above.