\s+ is not equivalent to \t because \s does not mean <space>, but instead means <whitespace>. A literal space (sometimes four of which are used for tabs, depending on the application used to display them) is simply . That is, hitting the spacebar creates a literal space. That's hardly surprising.
\s\s will never match a \t because since \t IS whitespace, \s matches it. It will match \t\t, but that's because there's two characters of whitespace (both tab characters). When your regex runs \s\s+, it's looking for one character of whitespace followed by one, two, three, or really ANY number more. When it reads your regex it does this:
\s\s+

Debuggex Demo
The \t matches the first \s, but when it hits the second one your regex spits it back out saying "Oh, nope nevermind."
Your first regex does this:
\s\s*

Debuggex Demo
Again, the \t matches your first \s, and when the regex continues it sees that it doesn't match the second \s so it takes the "high road" instead and jumps over it. That's why \s\s* matches, because the * quantifier includes "or zero." while the + quantifier does not.
\tis the escape sequence for tab only.\sis the special escape for space, tab, newline etc.\s\s+you are looking for a space followed by 1 or more spaces. It will not match\tNadya, in fact it won't match any letter at all.\s\s+matches a whitespace character followed by one or more whitespace characters. I know that's what you meant, but it's important to be precise in your phrasing when you're talking to regex beginners.