How similar are the English Opening and the Sicilian Defence?

Only the King's English 1. c4 e5 is supposed to be similar to Sicilian.

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After 1.c4 e5 the same pawn structures can arise. For example:

In the position with colors reversed there are some differences. For one thing White is a tempo up which might seem like it can only be good. But this extra tempo can actually give Black some advantages as well. White is also able to attempt to take advantage of the fact that he hasn't had to move his d-pawn. The extra tempo also means that Black is too slow to attempt any kind of opposite side castling attack.

It's possible to attempt to play almost any sicilian with colors reversed provided that Black plays ...d5 and goes into open lines.

1.c4 c5 can lead to similar positions too. You can go directly into the Maroczy bind or even get a Maroczy bind with colors reversed. Sometimes you get familiar sicilian structures but the White pawn is on c4 instead of e4 which can change the nature of the positions.

Some players also get into the closed sicilian with reversed colors after 1.c4 Nf6 2.Nc3 g6 3.g3 Bg7 4.Bg2 O-O 5.O-O d6 6.d3 e5 or the reversed gran prix attack after 1.c4 e5 2.Nc3 Nc6 3.g3 f5.

They really are NOT SIMILAR AT ALL!

Even 1.c4 e5 compared to 1.e4 c5.  The problem is that most reverse openings, the extra move makes a huge difference.  Not a huge difference in the sense that White wins with the extra move.  But the whole idea behind what both sides plays.

For example, since we are dealing with the English and Sicilian, I think everybody knows that the Sicilian Defense holds a slight disadvantage for Black (What sound opening doesn't?).  Having the extra move for White doesn't only shift the assessment from slightly better for the player that pushed the e-pawn to a miniscule advantage for the advancer of the c-pawn, but the entire game is different.

Take the Dragon for example.  White's most popular line against it, by far, is the Yugoslav Attack.  Very few people ever play the Classical Dragon any more.  Everyone goes Yugoslav.  Many English books will refer to one specific line as the "Reversed Dragon", namely 1.c4 e5 2.Nc3 Nf6 3.g3 d5 4.cxd5 Nxd5 5.Bg2 (or some garden variety of this - move order may be slightly different, but White will play d3 and O-O at some point in time - I am not a Dragon guru, but I know the basics of it).  Have you ever seen Black try to play the Yugoslav Attack?  I'd hope not.  Being behind the move is enough to make this line of play HORRIBLE for Black.  Normally, Black has to resort to a Reversed Classical Dragon, with the Bishops going to e6 and e7 (similar to e3 and e2 for White), castle Kingside (just like White in the Classical Dragon), etc.  Black should be able to equalize with correct play.

These major differences apply everywhere.  The King's Indian Attack is NOTHING like the King's Indian Defense outside of White's pawn structure and piece development after half a dozen moves.  Black often plays for f5 in the KID.  White usually plays h4 rather than f4 in the KIA.  In the KID, White is often attacking d6.  In the KIA, Black is usually after a Queenside pawn storm and creating problems on the b- and a-files.  Occasionally he may go after d3, but it almost never works.

The London and Slav are not the same.  The Colle and Semi-Slav are not the same.  The Nimzo-Larsen is not the same as the Nimzo-Indian or Queen's Indian.  Etc.

One is when White plays it, one is when Black plays it.

I think while White plays c4, he can get the early move advantage by attacking. But when Black plays it, it mostly leads to unclear and critical positions with even attacking chances for Black..

I think what you've made clear here is that whoever plays cpawn has an advantage in both these openings. 

Being a move ahead and yet there are equal attacking chances for the c5 player.

Being both a move ahead and the c4 player is crushing, its interesting to see how little its been analysed in comparison to e4 lines.

Also the priciple of not exposing the king and fighting for the center without risking material stands in both. 

Not very similar. The King's English is necessarily more positional and generally slower than Sicilian lines, black being a move behind.