Let $Y$ be a Young diagram. A filling of $Y$ is a labelling of the boxes in $Y$ by positive integers. For example, consider the Young diagram with shape $\lambda=(4,4,2,1)\vdash 11$.

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One filling of this Young diagram is

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A filling is a Young tableau if it includes each label from $1$ to $n$ exactly once. One Young tableau with shape $\lambda$ is

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Each Young tableau with shape $\lambda\vdash n$ corresponds to a set partition of $[n]=\{1,\dots,n\}$.

A filling is a semi-standard tableau if the labels monotonically increase in each row and strictly increase in each column. One semi-standard tableau with shape $\lambda$ is

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Finally, a semi-standard tableau is a standard Young tableau if it includes each label from $1$ to $n$ exactly once. Hence a standard Young tableau is both a semi-standard tableau and a Young tableau. One standard Young tableau with shape $\lambda$ is

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There is some variation in this terminology. For example, Fulton uses the terms tableau and Young tableau interchangeably for what we call a semi-standard Young tableau.