Intriguingly, there's reason to believe the R1 distills are nowhere close to their peak performance. In the R1 paper they say that the models are released as proofs of concept of the power of distillation, and the performance can probably be improved by doing an additional reinforcement learning step (like what was done to turn V3 into R1). But they said they basically couldn't be bothered to do it and are leaving it for the community to try.
2025 is going to be very interesting in this space.
Base models are general purpose language models, mainly useful for AI researchers and people who want to build on top of them.
Instruct or chat models are chatbots. They are made by fine-tuning base models.
The V3 models linked by OP are Deepseek's non-reasoning models, similar to Claude or ChatGPT4o. These are the "normal" chatbots that reply with whatever comes to their mind. Deepseek also has a reasoning model, R1. Such models take time to "think" before supplying their final answer; they tend to give better performance for stuff like math problems, at the cost of being slower to get the answer.
It should be mentioned that you probably won't be able to run these models yourself unless you have a data center style rig with 4-5 GPUs. The Deepseek V3 and R1 models are chonky beasts. There are smaller "distilled" forms of R1 that are possible to run locally, though.