Had Moses changed something in the Law as when Deuteronomy 12:15 - 16 is compared to Leviticus 10:10 and 11:4-8?
The simple answer is no.
First of all, let us look at the texts in question more closely.
15 “However, you may slaughter and eat meat within any of your towns, as much as you desire, according to the blessing of the Lord your God that he has given you. The unclean and the clean may eat of it, as of the gazelle and as of the deer. 16 Only you shall not eat the blood; you shall pour it out on the earth like water. - Deuteronomy 12:15-16
8 Then the Lord said to Aaron, 9 “You and your sons are not to drink wine or other fermented drink whenever you go into the tent of meeting, or you will die. This is a lasting ordinance for the generations to come, 10 so that you can distinguish between the holy and the common, between the unclean and the clean, 11 and so you can teach the Israelites all the decrees the Lord has given them through Moses.” - Leviticus 10:8-11
4 “‘There are some that only chew the cud or only have a divided hoof, but you must not eat them. The camel, though it chews the cud, does not have a divided hoof; it is ceremonially unclean for you. 5 The hyrax, though it chews the cud, does not have a divided hoof; it is unclean for you. 6 The rabbit, though it chews the cud, does not have a divided hoof; it is unclean for you. 7 And the pig, though it has a divided hoof, does not chew the cud; it is unclean for you. 8 You must not eat their meat or touch their carcasses; they are unclean for you. - Leviticus 11:4-8
In all three biblical quotes, Moses is in the mists of defining and explaining what the Law allows and does not allows when it comes to dietary rules for the People of God.
First of all, Moses explains that both clean and unclean amongst the Ancient Israelites may eat the (clean) flesh of animals, which are permitted to be eaten. Here he is simply making a statement. Both those who are clean and those whose are ritually unclean may eat the flesh of animals, but not their blood. Sorry, no blood sausage is permitted. The blood of animals must be poured on the ground.
In both the Leviticus quotes, Moses explains what constitutes is permitted to be eaten or drunk according to the rules of the Law.
For example, if one wishes to go into the tent of meeting, one must not drink fermented beverages prior to doing so. Doing so will make one common and unclean.
The last quote involving Leviticus, Moses is explaining what constitutes unclean animals which may not be eaten by the Chosen People. Again eating unclean animals will make one ritually unclean according to the Law.
I like to look at Moses division between clean and unclean animals as something of being done as a medial officer to keep the People of God healthy. For example, pigs are notorious for passing on worms to other hosts, people included.
Swine flesh if eaten by non-Jewish people must always be well cooked to avoid any contamination from various parasites of this animal. Moses is simply keeping the Ancient Israelites pure and healthy through dietary edicts!
To stay clean do not eat unclean animals!