Hi Peter

I could not find any evidence that they are the same, however It looks like it is.
There is no other birth or death for Henry Frederick Smith. Thomas and Annie Theresa Collyer also had son Thomas Hardwick Smith in 1830.
The IGI has the original copy of the burial there are about 20 on the page , and Henry Frederick is the only one without an age - most unlucky.
There was a fair amount of Cholera on the Island in 1832-33 , I read somewhere that a "C" was put next to the burial information when someone died from Cholera , there is no "C" next to Henry.
Thomas senior is shown as a "Gentleman"
The two children were "privately baptised"
None of the four are on the Isle of Man at the 1841 census

Cheers
David Dwyer