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I am new to Tikz and during some experiments I ended doing something like the example below but I can' quite understand why is there a space left between my two lines...

documentclass[tikz,border=10pt]standalone
usepackagetikz

begindocument
begintikzpicture[every node/.style=inner sep=0,outer sep=0]
 node at (0,0) (test) tikz draw (0,0) -- (1,0);;
 draw (test.east) --++ (1,0);
endtikzpicture
enddocument

It is very simple example of what I wanted to do and maybe I took it the wrong way and should not proceed this way but I would love to know if it possible to eliminate this space or not.

This is an interesting case! I originally thought it was due to the fact that, as @Andrew says in a comment, node has a border. However, that border can be removed by setting inner sep and outer sep to 0 and this is exactly what you do. So the node does not have a border.

What is going on is that the inner tikz picture has a border. Exactly why this is so is quite subtle. When TikZ builds a picture then internally it keeps track of the size of that picture. The main way of doing so is to keep track of a rectangle that is big enough to contain every coordinate that has been used, this is enough to ensure that every path is inside the picture (there are some questions about this with relation to Bezier curves which are an interesting read). However, when a line is drawn then it is drawn with a thickness and so if a path goes between, say, (0,0) and (1,0) then its maximum height will actually be a half linewidth above 0. So when TikZ adds a point to the bounding box, it actually adds a half linewidth beyond it. So when you create a picture with coordinates (0,0) and (1,0) and (for ease of explanation) line width 2mm, the bounding box will have corners (-.1,-1.) to (1.1,.1). And this extends a bit beyond the line.

When this is embedded in another node (I would go one stronger than @Andrew and say that nesting TikZ pictures should be avoided), the outer TikZ doesn't know anything about what the inner TikZ drew and just knows about the box size. So it creates a node big enough to contain that box. Even though you make that node as tightly fitting as possible (via inner sep=0, outer sep=0) you don't make it touch the inner line.

The solution proposed by @AboAmmar gets round this by making the line in the inner TikZ picture extend to the boundary of the inner picture since line cap=rect ensures that the line extends by half a line width beyond the coordinate. This works in the case of horizontal/vertical lines as then the overreach of the line exactly matches the excess added to the box, but the situation with a diagonal line might need more adjustment.

(I'm actually going to remember this one as another example of why nesting tikz pictures can cause strange effects and therefore is Not A Good Idea. If you have a situation where you think you need to nest tikz pictures, please ask here first and someone will come up with an alternative solution!)

In this particular case, you can add line cap=rect and that tiny gap will disappear.

documentclassarticle
usepackagetikz

begindocument

begintikzpicture[every node/.style=inner sep=0,outer sep=0, line cap=rect]
 node at (0,0) (test) tikzdraw (0,0) -- (1,0);;
 draw [inner sep=0,outer sep=0](test.east) --++ (1,0);
endtikzpicture

enddocument

At 1200% zoom:

As written in my comment and Loop Space's nice answer, nesting tikzpictures should be avoided. The standard way to do that is to work with saveboxes. Of course, a node has a border given by the line width.

documentclass[tikz,border=10pt]standalone
usepackagetikz
newsaveboxTikzBar
sboxTikzBartikz draw (0,0) -- (1,0);
begindocument
begintikzpicture[every node/.style=inner sep=0,outer sep=0]
 node at (0,0) (test) useboxTikzBar;
 draw (test.east) --++ (1,0);
endtikzpicture
begintikzpicture[every node/.style=inner sep=0,outer sep=0]
 node at (0,0) (test) useboxTikzBar;
 draw ([xshift=-pgflinewidth/2]test.east) --++ (1,0);
endtikzpicture
enddocument

As you see, once you avoid the nesting of tikzpictures, the gap is almost gone, and if you correct for the border by moving the line closer by -pgflinewidth/2 it disappears completely.