Signature according to English law is a mark of any sort made with the intention of signature.
Electronic signatures may be as simple as typing "signed" and a, hopefully your, name thereafter, but that is better described as a signature. Electronic signature generally means some form of cryptographic technique capable of being used to demonstrate that the content of the message or document is the same as when it was signed, and that it is reasonably impossible for anyone who does not hold the signing key of the signatory to have made the signature. The Pretty Good Privacy (PGP) cryptographic system and the GNU Privacy Guard (gpg) program which implements it are good for these purposes as well as others.
"Written signature" is sometimes heard. Again according to English law, if you can read it, it is in writing. A written signature to a document in writing may therefore be a gpg cryptographic signature accompanying a word-processor file.
(This is not legal advice)
Do not sign anything which you do not know or reasonably believe to be true. Doubly do not sign anything which you know to be untrue. Apart from moral considerations, the share of the gains from it you might be offered is unlikely to compare at all well with the possible lost earnings of the rest of your career. If you feel a need to sign a form which is substantially but not perfectly correct, use your pen to edit it until it is all true, add qualifications, write an essay if need be.
GPG may be obtained from http://gnupg.org/ for several operating systems. PGP implementations are provided by at least one company. IBM offer a commercial electronic notary service, and the GNUmedic project implemented the GNotary system to provide a means of demonstrating that the signature presented later is the signature made at the time asserted, a core function for systems secured by signature. This is available free and may be implemented and supported by any IT support organisation.