The word dimension has many dimensions of meaning. The basic meaning of a dimension is an independent component of something. For example, color is often considered to have three dimensions: chroma, hue, and value.
Mathematically, a dimension is one of a minimal set of independent components of an abstract space. There are many applications of this concept. For example, principle components analysis (PCA) is a technique that takes multivariate data and finds the uncorrelated components, which are the dimensions of the data.
In everyday usage a dimension is one of a minimal set of directional components, that is, linear measures from a center point. In this sense there are three dimensions in the world we inhabit. Time is often added as “fourth dimension” but it is not a fourth direction since there is no fourth direction. If time adds any dimensions to space, they must be some other kind of dimension.
A ruler can be oriented in three dimensions. So can a clock. You say a clock is the same clock in each dimension, so there’s no difference? That’s also true for a ruler: it’s the same ruler oriented in each dimension. As a ruler cannot be oriented in three dimensions simultaneously, so a clock cannot be oriented in three dimensions simultaneously. The simple conclusion is that there are three dimensions for rulers and for clocks.
Both space and time are three-dimensional, and they are the same three dimensions. These three dimensions may be characterized linearly or planarly because of the duality between lines and planes. Space is associated with linear (interval) measures. Time is associated with planar (circular) measures. No additional dimensions are needed to characterize both.