As many people have pointed out, you got caught in the middle of a battle between two crypto-currency advocate groups and the resulting confusion is why you aren't seeing your money.
Some useful knowledge for the future...
BITCOIN started in the year 2009. At that time (and all the way until half way through the year 2017) there was only one viable cryptocurrency called "bitcoin". As such, both the bitcoin.ORG website and the bitcoin.COM websites would have given you information and access to the same type of bitcoins.
In mid 2017 there was an inability to reach a consensus on new changes to the bitcoin system. The owner of the bitcoin.COM sided with those that implemented some changes resulting in a split of the system. The result is two VERY SIMILAR but INCOMPATIBLE cryptocurrencies. The currency that was supported by the owner of the bitcoin.COM has become known as BITCOIN CASH. The currency that is still supported by the owner of bitcoin.ORG is most commonly just called BITCOIN (although some will refer to it as BITCOIN CORE.
However, those that support and believe in the legitimacy of the BITCOIN CASH system think of their system as the "real" Bitcoin. They will often refer to their system as "BITCOIN" instead of "BITCOIN CASH". In some cases, the confusion is unintentional. In some cases it is intentional, but not malicious. In some cases, it is malicious and intentional.
So, what you purchased was "BITCOIN CASH" from the bitcoin.COM, but then you tried to send it to a wallet that operates on the system supported by bitcoin.ORG. There are so many similarities between the two systems that the sending service wasn't able to determine that the address you provided was from the other system, so it just sent the BITCOIN CASH coins and assumed you'd be able to access them. Meanwhile the wallet that you are using doesn't operate on the Bitcoin Cash system, so it is unable to see or access the coins itself.
The two systems are similar enough that if you can figure out how to export the private key from the Bitcoin wallet, and then import that same private key into a Bitcoin Cash wallet, the Bitcoin Cash wallet will be able to see and access the coins.
After that, you'll need to decide whether you want to keep the Bitcoin Cash coins, or if you want to exchange them for the Bitcoins of the other system. That decision will depend on why you acquired them and what you are planning on using them for, as well as your personal opinion about how you feel about each of the systems and their supporters.