Hiragana and katakana both originated from kanji forms that were used phonetically, back when Japanese first adopted Chinese characters and had no other syllabaries. The chosen phonetic kanji were eventually simplified down to become the kana that are standard today, and many hiragana were simplified from different kanji than their katakana forms, or were simplified in a different manner, which is why most hiragana and katakana don't look similar to each other.
In the case of へ, both the hiragana and katakana forms are simplified from the same character, 部, and happen to have been simplified in the same way, so they look the same.
There are some nice charts from Omniglot showing the origins of hiragana and katakana so you can compare:
The omniglot charts are helpful, but leave a lot to be desired. Ideally, the hiragana chart would show evolution from the handwritten kanji down to grass style so you can see how 書道家 slimmed down the character to its hiragana form, and the katakana chart would highlight the strokes from the original kanji that wound up in the katakana character.
As far as へ and ヘ are concerned, they are identical in many fonts, but they are coded as different glyphs, so a font designer can make them slightly different if they want to.