Some websites online show the fifth stroke as a vertical line straight down connected to the sixth stroke, while others (and in Chinese) have it as a downward diagonal dash. Is there are difference between the two?
Similarly, is the first stroke in 高 connected to the second or a diagonal dash?
Is this always the case whenever a Kanji has something similar to these two?
It's the difference between printing, handwriting, and calligraphy.
This element, called nabebuta or keisankanmuri (亠), should be connected and vertical for more formal (printed) styles, and will normally be disconnected and 'diagonal' for calligraphic styles and many handwritten styles.
There is not right or wrong unless you are talking about a particular font style.
When practicing kanji early on, it is normally recommended to stick to a more 'standard' style, like Kyokashotai (thanks @drooze).
For the Kanji 校 is the fifth stroke connected to the sixth stroke?
Depends on the country's prescribed standard.
Some websites online show the fifth stroke as a vertical line straight down connected to the sixth stroke
Japanese regular script handwriting prescribes this shape to be taught in schools.
HG Kyokashotai
while others (and in Chinese) have it as a downward diagonal dash.
Actual handwriting (that you'll find outside of schools) will have a variation.
HG Hagoromo, close to a semi-cursive script style.
Chinese kids are also taught in schools to write in this way.
中華民國教育部標準楷書
Is there are difference between the two?
In terms of comprehension, no.
If you're taking a Japanese written exam, they might get picky and deduct marks.
