In short, there is no difference, they are both medical professionals who specialise in lower limb treatments. Always ensure that your podiatrist is HCPC registered (http://www.hpc-uk.org/check-the-register/), a requisite for all UK podiatrists.
The difference between the professions is geographical and historical. While chiropodist depicts foot specialists in the UK and Ireland, podiatrist is more internationally recognised. However, in 1993 acknowledging the extensive use of the term podiatry, the UK and Ireland officially introduced the term and now the two terms are used interchangeably.
Courses in the UK to qualify as a podiatrist involve a three year degree level course in Podiatry and hence most foot specialists will use the title podiatrist.