In this case there is no difference.
Usually, the difference would be one of timing:
I eat breakfast
vs.
I am eating breakfast
The former would be for a regular activity, the latter for what I am doing right now.
But when it is a large group of people, the two meanings merge somewhat; someone, somewhere, is using a cheque right now.
This type of wording is often used in requirements manuals, specifications, policies, and procedures. Each such document should clearly define its terms to avoid ambiguity.
If this is from a policy manual that you need to adhere to, you should clarify the exact meanings of these terms.
A somewhat "famous" set of specifications for geeks of the world is the RFC specifications used for the Internet specs and include typical definitions for these types of terms. Here's an excerpt from https://www.ietf.org/rfc/rfc2119.txt, for "MUST" and "SHOULD".
MUST - This word, or the terms "REQUIRED" or "SHALL", mean that the definition is an absolute requirement of the specification. [This is the equivalent of your "have to". - CoolHandLouis]
SHOULD - This word, or the adjective "RECOMMENDED", mean that there
may exist valid reasons in particular circumstances to ignore a
particular item, but the full implications must be understood and
carefully weighed before choosing a different course.
The RFC defines the following words/phrases: "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL".
Best Answer
I think although both can be used interchangeably and as @FumbleFingers mentioned, for practical purposes there's no difference. However, I think they're sometimes used differently, depending on the situation.
When you see them eating, they're in the process of eating and you'd usually (not always) say this while seeing them eat.
For instance: you're with a friend and you're watching them eat. You then whisper over to your friend "When I see them eating, I feel compelled to eat."
In this case you're generally saying every time you see them eat, you feel compelled to eat.
For instance: you're with a friend, and you're talking about them, and then you say "When I see them eat, I feel compelled to eat."