Sources
A source imposes a quantity on the network. Which quantity it imposes, and whether it does so exactly, determines how it enters the system of equations and what it costs.
Current sources are free, voltage sources are not
A current source imposes a known current into a node. Its contribution is entirely on the right hand side of the nodal equations, and the system matrix does not know it exists.
A voltage source imposes a relation between two node voltages, which is not a nodal equation at all. Nodal analysis has one equation per node expressing current balance, and there is no current variable for an ideal voltage source to appear in. The system is extended with the source current as an unknown and with the constraint that fixes the voltage difference, as described under nodal analysis. The matrix grows by one row and column per source, and the added diagonal entry is zero, so the extended matrix is no longer positive definite and cannot be factorised by methods that assume it is.
This asymmetry is the reason so many models are formulated as current injections even when what they physically represent is a voltage behind an impedance.
The Norton equivalent
A voltage source with a series resistance can avoid the extension entirely. Source transformation replaces a voltage $V$ behind a resistance $R$ with a current $V/R$ in parallel with the same resistance,
which contributes a conductance to the matrix and a current to the right hand side. No extra unknown, no zero on the diagonal, and the matrix stays the shape it would have had without the source.
The two representations are equivalent at the terminals, exactly, for any $R$ that is not zero. The choice is therefore numerical rather than physical, and the cost is that the source is no longer ideal: its terminal voltage falls with the current drawn. Where a genuinely stiff source is wanted, $R$ has to be made small, and a small $R$ means a large conductance, which is the same conditioning trade-off that appears in switches.
Sources that change over time
The simplest time-varying source takes its value from a generator, as described under signal processing blocks.
A ramp source is more specific: it holds one value, then moves to a second over a defined interval, and holds that. The subtlety is what happens when the ramp changes not only the magnitude and phase but also the frequency. Interpolating a frequency linearly and applying it as if it had always been in force produces a phase discontinuity at both ends of the ramp, because phase is the integral of frequency and not its product with time. Blending the frequency contribution in and out smoothly over the ramp interval avoids that, at the price that the frequency during the transition is not the linear interpolation it appears to be.
A profile source takes its value from a recorded sequence instead of from a formula, stepping through samples as the simulation advances. It is the right choice when the excitation comes from a measurement, and it carries the obvious constraint that the sample rate and the simulation step must be reconciled: a profile is silent about what happens between its samples, and the simulation will ask.
Controlled sources
A controlled source takes its reference from another quantity in the simulation rather than from a parameter or a clock. This is what allows a component to be built out of sources: a converter imposes a voltage its control law computed, and an interface between two solvers imposes a value the other side produced.
The distinction from a time-varying source is that the reference is not known in advance. Since the reference is read as an input rather than solved simultaneously, it is the value from the previous step, which introduces a delay of one step into whatever loop the source closes. For a control loop that is usually acceptable and always worth knowing about; for a coupling between two solvers it is the central property of the method, and it is the subject of branches where the same delay is used deliberately.