The difference, and why it matters to you
A sublet means the original tenant leaves temporarily and comes back — the tenancy stays theirs. An assignment means someone else takes over the tenancy entirely and the original tenant is gone for good.
Section 97(4) is the reason the distinction matters commercially: during a subtenancy "the tenant remains entitled to the benefits, and is liable to the landlord for the breaches" of their obligations. Your counterparty does not change. If the subtenant wrecks the place or stops paying, you look to your tenant.
Section 97(5): "A subtenant has no right to occupy the rental unit after the end of the subtenancy." A subtenant who stays on is an overholding subtenant, not a new tenant, and section 98 gives the routes for dealing with that.
On an assignment the new person becomes the tenant, at the existing rent. That last part is why assignment requests are refused more often than they should be — and why refusing badly is costly.
The seven-day clock on assignment
Section 95(2) and (3) split the request in two. A general request — will you consent to an assignment at all — can be consented to or refused. A specific request naming a potential assignee can be consented to, refused as to that person, or refused outright.
Section 95(5) is the constraint: a landlord "shall not arbitrarily or unreasonably refuse consent to an assignment of a rental unit to a potential assignee". You can decline the concept in general; declining a specific, suitable person needs a reason that stands up.
Section 95(4) then attaches a consequence to silence. A tenant may give notice of termination under section 96 within 30 days of the request if the landlord refused a general request, refused a specific assignee under clause 3(c), or "does not respond within seven days after the request is made".
Read that plainly: ignoring an assignment request for a week hands the tenant an early exit. If your intention was to keep the tenant, silence achieved the opposite.
What you may charge
Section 97(3): "A landlord may charge a tenant only for the landlord's reasonable out-of-pocket expenses incurred in giving consent to a subletting." Actual costs incurred, and nothing more.
There is no administration fee, no premium, and no rent increase attached to granting consent. Section 134's prohibition on additional charges sits behind this.
Section 97(6) applies the section to all tenants — periodic, fixed, contractual or statutory — with the single exception of a tenant of superintendent's premises.
How to handle a request without losing the tenancy
Answer within seven days, in writing, even if the answer is that you need more information. The clock in section 95(4) runs on responding, and a holding reply is a response.
Ask for what you would ask any applicant, and apply the same standard you applied to the current tenant. A refusal that cannot be explained by reference to the person is the definition of arbitrary.
Log the request date. Almost every dispute here turns on when the request was made, and it is usually made in a text message that nobody filed.
If you would rather have the unit back than assign it, be aware that refusing is exactly what gives the tenant the right to leave on short notice — which may be the outcome you wanted, at the existing rent's end.