How animal cell types, tissues, and regional body plans arose is a fundamental question in EvoDevo. Many current efforts attempt to link genetic information to the morphology of cells, tissues and regionalization of animal body plans using single-cell sequencing of cell populations. However, a lack of in-depth understanding of the morphology of non-bilaterian animals remains a considerable block to understanding the transitions between bilaterian and non-bilaterian cells and tissues. Sponges (Porifera), one of the earliest diverging animal phyla, pose a particular challenge to this endeavour, because their body plans lack mouths, gut, conventional muscle and nervous systems. With a goal to help bridge this gap, we have studied the morphology, behaviour and transcriptomics of cells and tissue types of an easily accessible and well-studied species of freshwater sponge, Ephydatia muelleri. New features described here include: a polarized external epithelium, a new contractile sieve cell that forms the entry to incurrent canals, motile cilia on apopyle cells at the exit of choanocyte chambers, and non-motile cilia on cells in excurrent canals and oscula. Imaging cells in vivo shows distinct behavioural characteristics of motile cells in the mesohyl. Transcriptomic phenotypes of three cell types (cystencytes, choanocytes and archaeocytes) captured live indicate that cell-type transcriptomes are distinct. Importantly, individual archaeocytes show a range of transcriptomic phenotypes which is supported by the distinct expression of different genes by subsets of this cell type. In contrast, all five choanocyte cells sampled live revealed highly uniform transcriptomes with significantly fewer genes expressed than in other cell types. Our study shows that sponges have tissues whose morphology and cell diversity are both functionally complex, but which together enable the sponge, like other metazoans, to sense and respond to stimuli.