An invoice is a request for payment that contains information necessary to remit payment to the issuer. Normally that would include the issuer's name, address, terms of payment and if necessary an account number. The invoice also is given a number - a unique key identifier with respect to the issuer.
Later, this number can be referred to in future correspondence. A bill may or may not include any of the above, but an invoice usually will.
Rather, the distinction between these two words is more a matter of custom and the business in question being transacted. For example, a lawyer bills a client, for billable hours. In the abstract, "you should pay your bills on time." Work that is commissioned will usually generate an invoice.
Bill in the sense we're discussing is Anglo Saxon and dates from the 1400s, and invoice is French (envoyer, "dispatch") from the 1500s. You might make the case that invoices are attached to things that are delivered, but in practice it seems that various trades over time have selected one term or the other by tradition and custom.
Close and near can be used as adjectives, and in many cases they are the same when talking about physical distances.
The train station is close.
The train station is near.
They are not the same when talking about more abstract concepts, like relationships.
My mother is close [she is 3 feet away].
My mother and I are very close [we have a strong family bond].
My mother is near [she is 3 feet away].
My mother and I are very near [we are 3 feet apart].
Only near can be used as a preposition without the word to.
*We are close the train station.
We are close to the train station [correct: close to is the proposition].
We are near the train station [correct: near is the preposition].
When you convert to adverb form, they are not interchangeable at all. In this case, closely implies "at a small distance", while nearly implies "almost but not quite"
*We are nearly following the news.
We are closely following the news.
*I closely hurt myself.
I nearly hurt myself.
* incorrect usage
Best Answer
Any of those words would be suitable to convey the meaning of what you are trying to say, but there are subtle differences.
The words near and close are interchangeable, however the difference is that close implies a direct proximity, whereas near conveys more of a being in the same general area.
To show the difference:
With no other information, this would make one think that the stranger is almost touching the person, and invading their personal space.
This would be used more to describe someone who might be blocking the person's view.
The difference between them and nearby depends on who or what you are saying it in context to.
Using near/close would be if you are referencing the speaker/narrator, whereas nearby would be used if you are referencing the other object.
To use your examples, the correct words to use would be:
This is used because you are speaking with the pharmacy as the subject.
This is used on this occasion because the speaker is the subject, and not the bank.
These would not be used the other way round, unless you changed the subject of the sentence.
For example: