Q:

Is there any difference between writing the katakana カ and the kanji 力?

The two characters I'm talking about here is the katakana "ka" (カ) and the kanji 力 as in [入力]{にゅうりょく}.
Just by looking at the two characters in digital text form, they seem to be written in the same way, except that the katakana version seems smaller. Does this mean that when I am writing Japanese I should also make it smaller? (Note that by smaller I don't mean this small: ゅ)
Also, in some fonts, I have seen the first stroke of the katakana version written without the tick at the end. It just draws a horizontal line then a vertical line like this:
  | 
------
  |  |
  /  |
 /   |

instead of this:
  | 
------
  |  |
  /  |
 /  \|

Can I consider the first way shown above as a "sans serif" version? In handwritten Japanese, can I write that as well?

A:

カ (katakana) and 力 (kanji) appear essentially identical. The existence of the "hook" at the bottom right of the character would not help you distinguish the two, no matter whether they are typewritten or handwritten.
Then why katakana カ looks a bit smaller? That is because making hiragana/katakana generally look a bit smaller than kanji is a common practice in Japanese handwriting, (artistic) typography, etc. For example, see these posters which make heavy use of typography, or these beautifully handwritten letters. Can you see how the beautiful balance is like between kana and kanji?
In many computer fonts for day-to-day needs, this difference is not very prominent, and カ (katakana) and 力 (kanji) may look exactly the same. But in some fonts, you may find that katakana/hiragana are generally rendered smaller than kanji. The same thing can be said for other similar kana/kanij pairs, like ロ/口, エ/工.
In handwritten Japanese, not everyone is an excellent calligrapher, and it's not really practical to care for the character size too much. Telling apart カ (kana) and 力 (kanji) is basically impossible. Until you become an expert, you can write these characters exactly in the same way.

