"Hoarseness" Vs "frog in one's throat"

Question

Do the two expressions/idioms:

1. to have a frog in one's throat
   
2. to be hoarse
   

mean the same thing or they have different connotations and usages? If they differ I wonder if you kindly let me know about the difference.

In order to define the possible nuances, I have made two examples. Please have a look on them and let me know which choice is not correct in each case's space and why:

Please imagine someone is going to give a speech and wants to express their apology before starting their statements. He says:

1- Excuse me; ________________; because of the cold.

a. I'm hoarse
b. I have a frog in my throat

2- Excuse me; in yesterday speech I spoke so loudly that_________________.

a. I'm hoarse
b. I have a frog in my throat

I think they mean exactly the same thing and in all similar cases in which someone has such a problem with their voice can be used. But I doubted and decided to receive your approval on it.

Answer 1

"Hoarse" is the standard term. "Frog in my throat" is a colorful idiom that is meant to infer that your voice sounds like that of a frog.

That being said, one's voice becomes "hoarse" generally from inflammation due to dryness, overuse, or illness:

I've had a sore throat since yesterday, which is why my voice is a little hoarse right now.

"Having a frog" may be due to a number of factors, such as inflammation or congestion.

Something I ate is making me phlegmy. Let me try to get rid of this frog in my throat before I talk more.

Personally, I avoid using idioms that are too colorful, such as the aforementioned frog, as they tend to draw attention the idiom rather than on what I'm trying to say. But it's up to you.

(Edit) This does remind me of an old joke:

A man went to meet a rancher who was selling a purebred pony that the man thought his daughter might like. He got there and the pony was indeed quite a beautiful animal, the perfect size for a young girl, but he noticed as it romped around its corral that it didn't whinny, it just kind of coughed and rumbled in its throat.

The man asked the rancher, "What's wrong with that pony's voice?"

The rancher replied, "Well, he's just a little hoarse."