der Inhaber
owner
The person who owns a business, company, or shop; the proprietor.
Der Inhaber des Cafés begrüßt seine Gäste oft persönlich.
The owner of the café often greets his guests personally.

owner / holder
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owner
The person who owns a business, company, or shop; the proprietor.
Der Inhaber des Cafés begrüßt seine Gäste oft persönlich.
The owner of the café often greets his guests personally.

The noun 'Inhaber' (owner/holder) is derived from the verb 'innehaben' (to hold, to occupy), which means 'besitzen' (to possess) or 'bekleiden' (to hold an office). An 'Inhaber' is therefore literally a person who 'innehat' (holds) something, for example a business or a right.
Wer ist der Inhaber dieses Patents?
Who is the holder of this patent?
To specify what someone possesses, the genitive is very often used after 'Inhaber' (owner/holder). This construction is typical of formal and written language.
Der Inhaber des Restaurants hat die Speisekarte geändert.
The owner of the restaurant has changed the menu.
In a business context, typical combinations are 'Inhaber eines Geschäfts' (owner of a business), 'Inhaber eines Unternehmens' (owner of a company), or 'Inhaber eines Ladens' (owner of a shop). On the sign of a small business, you often see 'Inh.' as an abbreviation for 'Inhaber' (owner).
Der neue Inhaber hat den Laden komplett renoviert.
The new owner completely renovated the shop.
You can recognize this meaning by the fact that 'Inhaber' (holder) is combined with official documents, rights, titles, or records. Watch for words like 'Pass' (passport), 'Konto' (account), 'Lizenz' (license), 'Amt' (office), or 'Titel' (title).
Der Inhaber eines gültigen Führerscheins darf dieses Fahrzeug fahren.
The holder of a valid driver's license may drive this vehicle.
entrepreneur
'der Unternehmer' and 'der Inhaber' can both refer to a person connected with a business or company. 'Unternehmer' emphasizes that someone runs or founded a company, or takes economic risks. 'Inhaber' mainly emphasizes ownership: the person owns a shop, a company, a document, or a right. The words can be confused when someone is both the owner and the manager of a company. When the focus is on risk, leadership, and economic activity, 'Unternehmer' fits better. When it is only about ownership, 'Inhaber' is more precise.

Vor dem Termin muss der Inhaber des Ausweises das Formular unterschreiben.
Before the appointment, the holder of the ID must sign the form.
Der Unternehmer hat eine kleine Firma gegründet und stellt jetzt neue Mitarbeiter ein.
The entrepreneur founded a small company and is now hiring new employees.