These two phrases get swapped around constantly, including by people selling signing software. They aren't the same thing, and the distinction is worth five minutes because it changes what you should be asking for.
One is a legal category. The other is a piece of mathematics.
Electronic signature: the legal idea
An electronic signature is any data attached to a document that the signer intended to act as their signature. That's the definition, and it's deliberately broad. A typed name, a finger-drawn scrawl, a tick in a box, a click on a button labelled "I accept".
It's a statement about intention, not about technology. Nothing in the concept says anything about encryption, or keys, or file formats. If you meant it as your signature and it's in electronic form, it's an electronic signature. This is the category almost every business document lives in.
Digital signature: the mechanism
A digital signature is a specific cryptographic technique. Two keys, one private and one public. The signer's software takes a mathematical fingerprint of the document and encrypts it with the private key. Anyone holding the matching public key can check two things: that the fingerprint matches the document in front of them, and that it was produced by that particular private key.
What this buys you is tamper detection. Change one character in the document afterwards and the fingerprint no longer matches, and the signature reports as broken. That's a real and useful property. It's the reason banks and government systems use it.
But notice what it doesn't tell you. It says the document is unchanged and that a specific key sealed it. Whether that key genuinely belongs to the person whose name is on the page depends on who issued the key, how carefully they checked, and whether the holder has kept it to themselves. The cryptography is airtight. The bit where a human is connected to a key is where the weakness lives.
How they relate
A digital signature is one way to produce an electronic signature. All digital signatures used to sign documents are electronic signatures. Most electronic signatures are not digital signatures.
South Africa's higher tier, the advanced electronic signature, is where the two meet: it's built on digital-signature technology, but what makes it "advanced" in law is that an accredited provider verified the signer's identity before issuing the credential. The legal status comes from the accreditation, not from the maths.
Which one you actually need
For ordinary business documents (quotes, service agreements, NDAs, offer letters) you need a valid electronic signature and evidence of who applied it. Ask about the audit trail, because that's what a dispute turns on: which address the request went to, when it was opened, when it was submitted, and what the document said at that moment.
Cryptographic sealing is a good thing to have underneath, and decent signing tools do it, because it means nobody can quietly edit the signed PDF afterwards. Treat it as hygiene rather than the headline.
Where you genuinely need an accredited advanced electronic signature, you'll know, because a specific law will be demanding a signature. That's a narrow set of documents, and it involves going to an accredited provider rather than choosing a feature in some software.
The trap is a vendor waving "military-grade digital signatures" at you while offering nothing that records who signed. Sealing a document you can't attribute to anyone is a lock on a door with no walls around it.
E·BIZI Papers keeps the signed PDF sealed against later editing, and, more to the point, keeps the record of who signed it and when. That's the combination that holds up.