Not quite sure what you mean by "background check" but there is an increased level of disclosure required of conviction and other penalties for citizenship compared with ILR. For the latter, fixed penalty notices (such as speeding or parking tickets) need not be disclosed, but for citizenship they do.
ILR: (verbatim from the paper form SET-M)
You must give details of all criminal convictions, including spent convictions. This
includes convictions for road traffic offences, including drink-driving offences, but not fixed
penalty notices (such as speeding or parking tickets).
Citizenship: (verbatim from Guide AN Naturalisation Booklet The Requirements)
Fixed penalty notices (such as speeding or parking tickets) must be disclosed, although will not normally be taken into account unless:
• you have failed to pay and there were criminal proceedings as a result
• you received 3 or more fixed penalty notices at any level
• in the past 3 years you received 2 or more fixed penalty notices, at least one
of which was at the upper levels (fine of £200 or more).