If an invoice is for "accounting VAT" then the tax point is the same date as the VAT invoice (using the 14 day rule) whereas if a business is "cash accounting" for VAT, the tax point is the date when the money is received. "Accounting VAT" also known as "Standard accounting" is traditional practice and is what most businesses tend to use as you simply pay VAT on the invoices you raise and not when payment has been made (cash accounting). Find out more about the Cash Accounting scheme.
With standard accounting there is a general 14 day rule which applies to most businesses. For instance, if you raise an invoice within the first 14 days of delivering goods and/or services to your business customer then you simply input the date you sent the invoice regardless of if that date falls in a new month or VAT Quarter.
For example - 31st March is your 1st Quarter end and you send a product to a customer on the 25th March but you don't invoice your customer until the 2nd April (new Quarter) - you therefore use the 2nd April as your invoice date and do not back date it to the 25th March as it falls within the 14 day rule. This invoice will then be included in the second quarterly VAT return which began on the 1st April.
The usual practice is to send an Invoice for goods and/or services after the transaction is completed (unless you are sending a proforma) but before your business has been paid as it is essentially a demand for payment. If a customer pays you in full before you have raised an invoice it is not ideal and essentially creates a Tax Point i.e. the date at which VAT is liable which supersedes any invoice VAT accounting schemes.
Therefore regardless of whether the invoice was issued within the "14 day rule" or after payment was made then you would need to include the "Tax Point" date on the invoice so it is filed within the correct VAT quarter. You would then need to issue a receipt for payment which is separate to a VAT Invoice.