Difference between dimensionality reduction and clustering General practice for clustering is to do some sort of linear/non-linear dimensionality reduction before clustering esp. if the number the number of features are high(say n). In case of linear dimensionality reduction technique like PCA, the objective is to find principal orthogonal components(say m) that can explain most variance in the data such that m<<n when n is high. 
But for non-linear dimensionality reduction techniques like auto-encoders, can the reduced dimensions, itself be clusters that indicate different modes of operation example for industrial components. Am I missing something here or is my understanding of non-linear dimensionally reduction wrong? Any help is appreciated. 
This question might be too basic for some, so please don't be extremely critical of the question if you don't want to answer it. 
@fk128 shared his interpretation of my question that might be better understood and easy to interpret than what I have mentioned above
 A: The components of an autoencoder are supposedly even less reliable than your usual clustering.
Why don't you just try it: train autoencoders on some data sets, and visualize the "clusters" you get from the components?
While this great answer on tSNE for clustering is specific for tSNE, I believe the results for other such encoders will be similar: they will cause fake clusters because of emphasizing some random fluctuations in data.
A: There are two types of clustering: hard and soft. Hard is when you assign a specific data point to a single cluster/category. So if there are $k$ clusters, a data point $x$ can only be assigned to one cluster in  $\{1,..., k\}$. Soft/fuzzy is when a data point is assigned to multiple clusters, and the assignment is represented with membership weights, such that all the weights add up to 1. So for example if there are 3 clusters, a datapoint $x$ can have weights $w = [0.1,0.6,0.3]$ such that $0.1 + 0.6 + 0.3 = 1$. You can also use the weights representation in the hard clustering case, so you'd only have $w = [1, 0, 0]$, where one component is 1 and the rest are zero (this is also referred to as one-hot encoding).
Any sort of dimensionality reduction, linear or non-linear, reduces the dimensions of the input features from $n$ to say $m < n$. So if you have a data point $x$ with dimension $n$, it is transformed into a data point $x'$ with dimension $m < n$. 
Assuming I understand your question correctly, your question is whether with an auto-encoder the components of $x'$ can represent cluster membership weights, i.e. $x' = w$. However, this is extremely unlikely to be the case.
Typically, to obtain clusters, you can later run any clustering algorithm on the dimensionally reduced data, regardless whether it was obtained from a linear or non-linear dimensionality reduction technique.
A: In my opinion these are two distinct questions, please add  any citations that might clarift I find the question quite interesting
1) Difference between dimensionality reduction and clustering eg in PCA
The core difference between the 2 is:
a. Clustering = group rows together (often with useful properties eg i want group X elements to be similar to each other). = so for dataset size N with dimensionality D at the end  you will have M size (<N) with dimensionality D. -> reduce number of rows (data points)
b. Dimensionality reduction -> reduce the number dimensions ( = columns ). columns are not same as rows ie a vector with 2 or 3 dimensions and a vector with 1 dimension are both valid data - points.
2) But for non-linear dimensionality reduction techniques like auto-encoders, can the reduced dimensions, itself be clusters that indicate different modes of operation example for industrial components.
The autoencoder neural network architecture performs dimensionality reduction in its latentspace (assuming smaller number of neurons than input layer ) BUT  one could add further constraints to tranditionl MSE loss function.
Such a constraint could to force the latent space to be a one-hot vector forcing 1 neuron to be close to the scalar value of 1 and the rest to 0. Which can be considered a form of clustering.

Further thoughts
Dimensionality reduction and clustering are problems algorithms can be modified to solve many problem. AE in particular has been used as a component to more complex architectures (and with one layer AE performs linear mapping) that solve many different problems so keep an open mind before putting it to "boxes".
