Just going by what it says on Picture Sheffield, Tinsley Park followed on from the Christ Church churchyard and cemetery in Attercliffe. So they are different places geographically but they do have a link.
Picture Sheffield says that Christ Church churchyard closed for burials in 1856, and was replaced by a cemetery which was constructed very close to the churchyard.
Then because that cemetery was quite small a new site was opened at Tinsley Park in 1882.
Your relative was probably buried at Tinsley Park but the service took place at Christ Church Attercliffe. The Cemetery at the Church and just over the wall at the Attercliffe Municipal Cemetery is very small.
LEARY, Anthony (~, age 54).
Died at 17 Swan St; Buried on March 13, 1898 in ~ ground;
Grave Number ~, Section NC of Christ Church Cemetery, Attercliffe.
Parent or Next of Kin if Available: ~. Remarks: ~.
Plot Owner: ~ ~ of ~. Page No 180
As you can see from our transcription it states he is in NC section.
If you go back to our Burial Records (menu) and at the top of the page you will see one of the headers is listed as [Maps & Photos]. Click on it and you will find many maps of Sheffield Cemeteries.
The actual Plot number you will have to contact City Road Cemetery who looks after all Sheffield Municipal Cemeteries.
Tony Morton may have a photo of the headstone if there is one. Check out for this under the MI section over to the left.