People use the two phrases as if they mean one thing. Software vendors encourage that, because the confusion sells upgrades. The difference is small to explain and large in practice.
An electronic signature is any mark made with the intent to sign. A digital signature is a cryptographic operation that binds an identity to a specific file. One is a legal category and the other is a technology. You can want either without wanting the other. If you want to learn more about which free tools produce which, that guide lines them up next to the built-in options on each device.
What counts as an electronic signature
Almost anything, and the statutes are deliberately broad. US law calls it "an electronic sound, symbol, or process" attached to a record and "executed or adopted by a person with the intent to sign". A typed name is included. So is a drawn squiggle, and in the right context a clicked checkbox.
The EU draws the same line, then adds two tiers above it. An advanced electronic signature is uniquely linked to the signer and reveals any change made after signing. A qualified signature is an advanced one produced on a certified device, using a certificate from a provider that checked who you are. Article 25(2) of eIDAS gives that tier the same legal effect as a handwritten signature.
What a digital signature adds
Two things, and they are worth naming precisely. It confirms who signed, on the strength of a certificate issued by somebody who checked. It also shows whether the file changed afterwards, since the signature covers the bytes of the document.
Adobe puts it the same way in its documentation: a certificate-based signature identifies the signer and shows that the document has not been altered. The PDF profile for doing this properly is PAdES, defined in ETSI EN 319 142.
Why the drawn kind is usually fine
Most agreements never get disputed. When they do, the argument is usually about terms rather than about whether a signature is genuine. For those, a drawn signature plus the email thread that carried it is enough.
The calculation changes with high-value documents. It changes with a counterparty you have never met, and it changes when a regulator sets the format. In the EU, some property and public-sector work requires the qualified tier outright, and no free tool produces one.
A practical way to decide
Ask what you would need if the other side said "I never signed that". Sometimes the honest answer is an email thread and a date, and then a free signature on your own device is fine. When the answer involves a certificate and an audit log, pay for the platform that produces them.
One more thing worth knowing. Under the 2024 update to eIDAS, EU member states must offer a Digital Identity Wallet that lets people create qualified signatures free of charge for non-professional use. That changes the maths for private individuals in Europe, once the wallets reach people's hands.