There is a difference, and it could be important to how the circuit functions or doesn't function. Note, this does not apply to Schmitt trigger input components.
The T in HCT stands for TTL. While an HC part has a normal CMOS input stage transition level of approx. Vcc/2, An HCT part has TTL transition levels: Below 0.8 V is a 0, above 2.4 V is a 1, and anything in-between is not allowed and has unpredictable effects on the output state. So while an HCT part would see 2.4 V as a 1, an HC part could see it as a 0. Not good.
In fact, old TTL parts have a single input transition level around 1.8 V, and CMOS ouptut stages go all the way up to 5 V (as opposed to TTL parts that swing up to only about 3.5 V), but I don't think you can bank on that without analyzing the full circuit schematic to see who is talking to what. I wouldn't.
AND ...
Some HC parts are rated for operation down to 2 or 3 volts, while HCT parts are limited to - wait for it - TTL power rails.
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