Er, yes and . . . er, no!
The Criminal Records Bureau currently only provides two levels of disclosure. 'Standard' shows up all convictions, cautions, etc. 'Enhanced' show the same information, plus anything else which a senior police officer (or other relevant official) deems to be relevant.
So, officially, there's currently no such thing as a 'basic' disclosure. However many people loosely use 'basic' as synonymous with 'standard'.
To confuse the matter though, at one time the CRB proposed to introduce a third level of disclosure, which would (officially) be called 'basic'. The proposal was that (unlike the other levels) convictions would only be shown which weren't spent and also (unlike the other levels) would be available to all employers (and not just those within certain employment sectors). However that proposal seems to have been shelved.
NB: The foregoing applied in England & Wales. Scotland has a different system. (I'm not sure about Northern Ireland!).
Chris