What is the difference between a subnet mask and a netmask?

The difference is very, very slight. 9 times out of 10, they will mean the exact same thing.

However, the terms can have a contextual meaning in cases where we're discussing the subnetting of a given network. In those cases, the two terms "network mask" and "sub-network mask" can have distinct meanings. That is, if we make a distinction between a "network" and a "sub-network" then "the mask of a network" and "the mask of a sub-network" mean different things because of the context. This distinction is a relative distinction.

For example, let's say you've been issued the 10.10.0.0/16 network (using CIDR notation). Here, your "network mask" is 255.255.0.0. Let's say you need to separate this network into 4 smaller networks, each as large as they could possibly be. In order to get 4 networks out of 10.10.0.0/16, you need to borrow two bits (00, 01, 10, 11) from the host address and use them for the subnet addresses. This will give you the following sub-networks:

10.10.0.0/18
10.10.64.0/18
10.10.128.0/18
10.10.192.0/18

Here, your "network mask" is still 255.255.0.0, but each "subnet mask" is 255.255.192.0.

But, as I said, it's completely a relative term based on context. One could also talk about 255.255.192.0 being a "network mask" and then 255.255.0.0 being a "supernet mask" if in the same context we're talking about 10.10.0.0/16 being a supernet of, say, 10.10.64.0/18. It's all based on the context of what is being discussed.

The "Netmask", "subnet mask", or simply "mask" are all the same thing: A mask that tells software which IPs belong to that network an which don't.