Quotes:
"The offence of driving without due care and attention (careless driving) under section 3 of the Road Traffic Act 1988 is committed when the defendant's driving falls below the standard expected of a competent and careful driver - section 3ZA(2) of the RTA 1988"
"The offence of dangerous driving under section 2 of the Road Traffic Act 1988 is committed when the defendant’s driving falls far below the standard expected of a competent and careful driver and it would be obvious that driving in that way would be dangerous – section 2A of the RTA 1988."
[Source:
https://www.cps.gov.uk/driving-offences ]
While there is a specific offence of "causing serious injury by driving dangerously" (section 1A Road Traffic Act 1988), there's no specific offence of "causing injury by careless driving" (as in your post). Such an offence would be dealt with purely as "careless driving" but with the injury thus caused pushing the 'harm' factor (considered by the court when passing sentence) into the 'higher' category. See pages 114 to 116 here fo rthe sentencing guidelines:
https://www.sentencingcouncil.org.uk/wp-content/uploads/MCSG-April-2017-FINAL-2.pdf