I took a look at some of this and found index cards for 2 Joseph Winters:
http://www.digitalarchives.state.pa.us/archive.asp
The link below will lead you to both of them in 3 or 4 "clicks".
I uploaded images of both their cards but I am struggling to get them to post here.
http://www.digitalarchives.state.pa.us/archive.asp
Joseph #1 who served in the 15th (90 day) Inf. is problematic. His card says he was 40 at the time he enlisted in 1861. It also says he was born in 1841. This would obviously make him 19 or 20 in 1861.
It further states that he was discharged in 1867, when everything I've found says he mustered out with his Regt. on 8 Aug 1861.
I'd say that card is badly flawed, and not to be depended on without corroborating documents.
He is buried at Shoemaker Cemetery in Dalton, PA in Lackawanna Co. Is that where you posted the picture from?
Joseph #2 of Co. B, 56th Inf. was 22 years old when drafted in 1864 (could have been born in 1841)
(
https://pawchs.org/draft-list-sep-1864/)
He was drafted in the 13th District of Pennsylvania from Tunkhannock Twp. as recorded in the Wyoming Republican on 5 Oct 1864. That draft was held 29 Sep 1864.
So, although the 56th was at the Wilderness in May, Joseph didn't join them until much later. Nor was he at Gettysburg a year prior. (Unless serving in an Emergency Militia situation as suggested earlier).
If you have family evidence that Amanda was his wife, I'd say (by virtue of the pension card), that this is your guy.
Doesn't preclude Joseph #1 from being the same man. He may have served in 3 different units.
I noted that Joseph #3
20th Regiment, Pennsylvania Infantry Militia (Emergency, 1863 has the middle initial H.
Might be a helpful clue down the road.
I thought it was interesting to note that BOTH the 15th Inf and the 56th Inf were recruited in part in Luzerne County.
As you probably know, this county abuts to the south of Wyoming County where you originally stated your Joseph had enlisted from. And Lackawanna county (where Joseph #1 is buried lies directly east of, and abuts both Wyoming and Luzerne Counties.
Coincidence?