"I hope I can" vs "I wish I could" proper usage

• I hope I can go to the beach
• I wish I could go to the beach

Am I right to assume that both of these sentences are grammatically correct? And that their difference only lies in the meaning you want to convey?

For example, I will use "I hope I can" when I’m trying to say that there is a future possibility that I can go, or that there is a strong possibility it can happen (just not now).

But for "I wish I could", I will use that when I know that there’s no chance I could go, or there’s no chance it will take place.

…Or am I wrong?

I do know that grammatically, the following are wrong:

• I hope I could go to the beach (because ‘hope’ usually uses the present tense)
• I wish I can go to the beach (because ‘wish’ usually uses the past tense)