The short answer
A summons is a court-issued form of process associated with the start of an action and service of the initial pleading on a defendant. An initial pleading is the complaint, petition, or other first filing that states the claim or request and begins that party's involvement in the action. A subpoena is a legal command under Florida Rule of Civil Procedure 1.410 requiring a named person to attend, testify, produce specified material, or comply with another authorized demand stated in the subpoena.
Florida Statutes section 48.011, which addresses the statewide reach and direction of civil process, says summonses, subpoenas, and other process in civil actions run throughout Florida. It also says all process except subpoenas is directed to the sheriffs of the state. That distinction is one reason the document must be identified before a server is assigned. For broader context, read what service of process means in Florida.
Practical distinction: a summons connects a defendant to a newly commenced action and its initial pleading. A subpoena directs the named person to do what Rule 1.410 and the issued document require.
What a summons does
Florida Rule of Civil Procedure 1.070(a), which covers issuance of summonses and other process when an action begins, requires prompt issuance by the clerk or judge under that official's signature and the court seal. Rule 1.070(e), which covers delivery of the initial pleading, requires a copy of that pleading to be delivered at the time of personal service of process. Personal service means delivery made to the person to be served under an authorized method. It is not a synonym for every method Florida law may permit.
A prepared assignment should identify the issued summons, every pleading or document counsel wants served with it, the exact defendant name, address, deadline, and instructions. Pro Legal Serve performs professional service of legal documents and documents the assignment without deciding whether the papers are legally sufficient.