I've been trying to memorize some Kanji, and I've noticed that some of them seem to have different forms. So depending on what app I use, or what website I visit, the Kanji seems lightly different. As far as I can tell, they are actually the same kanji, just not always written the same.
To demonstrate what I mean, consider this screenshot from google image search:
Sometimes the kanji is written with the last horizontal stroke joined, sometimes it is separate.
Sometimes this kanji is written with the two verticle strokes on the bottom right as straight lines, other times as little arrows going to the left. Some google search results suggest the straight-line version is Chinese and the little-arrows version is Japanese, however one of my Japanese textbooks (Remembering the Kanji, vol 1) has the straight-line version.
Also this example: Sometimes I see this character with two horizontal lines in the top-right, sometimes I see it with three. This character is even more confusing because when I copy and paste that character I sometimes get the two-line version and sometimes I get the three-line version. Is this purely a font difference or is something more complicated happening?
The dictionaries I use (jisho.org, and a paper dictionary) tend to have just one form or the other, and does not reference the other form as an alternate form.
What is this kind of variation called? Like is there a name for it?
For two slightly different looking kanji, how do you know if they are actually different kanji or if they are just variations of the same kanji? Is this just a matter of experience, or is there a good list or a good set of rules somewhere?
Is this like the Japanese equivalent of how in english, the letters "a" and "g" are displayed differently depending on fonts. And letters like "b" and "p" may be written slightly differently (if you write fast, a lot of people don't join the loop properly in 'b' and 'p').
If you write in Japanese by hand, which form should you write? Are there conventions or rules? (e.g. in english, when you write the letter "a", it's always the comic-sans style 'a'). Or should I mentally treat them as the same symbol, and just write it however I feel like writing it?
Are there cases where kanji have more than two different forms?