Hi Judy
Yes the Glengarry is the hat. You really should be using Google to discover basic information like this. By two badges do you mean the one on the hat and the collar badges? If so, they just had different designs on different parts of the uniform.
If you search for his full name on Ancestry - it would be worth taking out the free 14 days subscription as there is quite a lot - you find a WW1 service record plus a WW1 pension record - although the penson record flows into that for another man.
He enlisted in 1915 into the Royal Engineers as a tunneler - he was a collier. He only lasted 5-6 months as he was invalided out But that was enough time to be sent to France. So there will be a medal card for him. He claimed he was 45 in 1915, but there is something in the record saying he was 55 years old. More interestingly he claims previous service with the South Staffs Regiment, being discharged 'term of enlistment' in 1891. If he was 21 years old in 1891 he could not have been a Regular, as they enlisted for 12 years after the age of 18. However he could have been in the Militia or VB, as they took men at 17 for four years.
His wife is Melinda (?) and children Raymond and Oliver. I could not find a birth on FreeBMD with Dudley as a middle name. But this could be added later. There is a William Smallman born in Dudley in June (qtr) 1862. I think you need to download the information on Ancestry, print it off and read it carefully.
Ken