Both of those calculations are correct. But, they look so different, it’s not surprising that you’re confused.
There are two things causing your confusion:
(1) the two calculations are presented in different formats, and
(2) in the first calculation, you are making a purchase and paying for it with dollars;
and, in the second calculation, you are making a purchase and paying for it with francs
(which, then, have to be exchanged for dollars).
(There’s a third issue here, which I will leave until the end of this post.)
Let’s re-write the second calculation, using the same format as the first calculation:
Notice that, in the second calculation, you did not earn $200 — you earned 200 francs.
So, how much is that in dollars? At the prevailing exchange rate of USD/CHF = 1.4550, one dollar = 1.4550 francs.
Therefore, 200 francs = 200 / 1.4550 = $137.46
In the second calculation in the School lesson, the pip-value ($6.87 per pip) was introduced in order to convert 200 francs to U.S. dollars.
The slight difference between $137.40 (in the School lesson) and $137.46 (which I calculated above) is due to rounding the pip-value down to 2 decimal places.
I hope that clears up the math for you.
About that third issue that I mentioned: In the spot forex market, currencies are not actually “bought” or “sold”.
If you were to visit the Foreign Exchange Department of a large bank, and actually exchange $11,800 for €10,000 (as in the first calculation in the School lesson) you would actually be “buying” euro, and paying for them with dollars.
Likewise, in my re-write of the second calculation (from the School lesson), a similar cash transaction was described — “buying” U.S. dollars, and paying for them with Swiss francs.
But, in the second calculation, as presented in the School lesson, a spot forex transaction was described. And, in such a transaction, there is no actual buying or selling of currencies or currency pairs. However, the terms “buying” and “selling” are firmly embedded in this business, and you will continue to hear those terms used, just as they were used in this School lesson.
For now, don’t worry about the fact that those terms are totally incorrect. Instead, concentrate on thoroughly understanding the math involved in figuring profits and losses.