Both replies could be deemed correct; it may depend on the target audience.

In Belgium, bankruptcy proceedings start with a 'dagvaarding' = summons, whereas in the UK they start with a petition = verzoekschrift. A copy of the petition must be served on the debtor (see my second ref).

I think asker is in the best position to decide which term will be best understood by the target audience of his text.

From what I've seen on the web, Adrian is right: 'bankruptcy summons' seems to refer to Irish law.

By the way, I do not understand Kirsten's explanation (sorry Kirsten) that 'bankruptcy is before a court, therefore it is a summons'. The difference between a dagvaarding (summons) and a verzoekschrift (petition) is that the former is addressed to the other party, whereas the latter is addressed to the court. However, both the 'dagvaardingsprocedure' and the 'verzoekschriftprocedure' are proceedings before a court.

https://www.citizensadvice.org.uk/debt-and-money/debt-soluti...
"Step 2: bankruptcy petition.
If you don't pay, negotiate a payment plan or get the statutory demand cancelled, the creditor will be able to apply for your bankruptcy by presenting a bankruptcy petition to the court.
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https://www.gov.uk/apply-to-bankrupt-someone
A bankruptcy petition is an application to the court for someone’s assets to be taken and sold to pay their debts.
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Belgische Faillissementswet http://www.ejustice.just.fgov.be/cgi_loi/change_lg_2.pl?lang... :
Art. 6. Onverminderd de bepalingen van de wet (...) geschiedt de faillietverklaring bij vonnis van de ondernemingsrechtbank waarbij de zaak aanhangig is gemaakt (...) op dagvaarding van een of meer schuldeisers, van het openbaar ministerie (...)
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In the UK, the term writ of summons has been replaced by 'claim form' and if I'm not mistaken, summonses are issued to start criminal proceedings.

https://uk.practicallaw.thomsonreuters.com/3-107-7346?transi...

Summons
In relation to criminal proceedings, a court order directing a defendant to appear before a magistrates' court made under section 97 of the Magistrates' Courts Act 1980.
In relation to civil proceedings, see Application notice.
Application notice
Formerly known as a summons. A document in which the applicant states their intention to seek a court order (see Civil Procedure Rule (CPR) 23.1).