Different card providers have different ways of presenting data using their online platforms when it comes to miles and points.
American Express are very clear: on the BAPP, you earn 1.5 Avios per pound on everything except BA spend, which is double. This is shown on the statement like this:
The £5.39 in Tesco is multiplied by 1.5 and rounded to the nearest whole number, giving 8 Avios. Likewise, the £17.50 spend at BA is multiplied by 3 and and rounded, giving 53 Avios.
Barclaycard, on the other hand, just lump them together on the statement and send them across to IHG.
On your IHG statement, these are broken down into Visa, international and hotel spend, the former on the Black card earns 2 points per pound with the other two earning 4 points per pound.
In order to check if the tally is correct, you need to download a .csv file of your statement, remove any payments and then round down the entries to whole numbers. You can do this automatically in Excel using the formula =ROUNDDOWN(G2,0) where G2 is a cell reference, and 0 is number of decimal places you want. Then you multiply everything by 2 if it is normal spend or by 4 if it is international or hotel. This figure should roughly tally with the one on your IHG account. If it is a few out wither way I would not worry, as it is likely to be a rounding up / down issue. However, if it more than a hundred out,then it is worth getting in touch with them and asking them to look at it in detail. Of my last 12 statements, 10 were spot on; the other 2 were way out, so I have asked them to take a look and will report back with the outcome.
Have you noticed any discrepancies on your IHG Statements? What have you done about it?