I am confused between vector and matrix

I am a beginner in the machine learning field and while learning the tensorflow introductory I understood that tensor is just nothing but a generalized name for quantities that require multiple variables (features) for it’s description.

Then there is this line -> Matrix and Vectors are the tensors with different rank. Matrix is 2d tensor and vector is 1 d tensor.

I then searched for the difference between Matrix and Vector and this text confused me

A vector is a matrix with just one row or column

And later in the tensor’s definition

A tensor is often thought of as a generalized matrix. That is, it could be a 1-D matrix (a vector is actually such a tensor)

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I am coming from the CS background where I have learnt that 1D is array 2D is matrix and we used to take 1D array like std::vector<float> height_vector

So what is difference between arr[10] and arr[1][10] or arr[10][1] ?