
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.

holder
The person who is in possession of an official document, a title, an office, or a right.
Der Inhaber des Passes muss persönlich zur Botschaft kommen.
The holder of the passport must come to the embassy in person.
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
Unternehmer and Inhaber can refer to the same person. Unternehmer emphasizes that someone is engaged in business and bears responsibility and risk. Inhaber primarily says that the business or company belongs to them; whether they run it themselves is not the focus.

Herr Klein ist Inhaber der Bäckerei, weil sie ihm gehört.
Mr. Klein is the owner of the bakery because it belongs to him.
Herr Klein ist Unternehmer, weil er die Bäckerei selbst führt und das wirtschaftliche Risiko trägt.
Mr. Klein is an entrepreneur because he runs the bakery himself and bears the financial risk.